P. Nikitas

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.

On the equations describing chromatographic peaks and the problem of the deconvolution of overlapped peaks

The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.

Thermodynamic methods for analysis of adsorption data of organic compounds at electrified interfaces

Abstract The thermodynamic methods used for analysis of adsorption data at charged interfaces are reviewed critically. It is shown that the conventional methods depend the validity of their results upon the choice of the molecular model of the adsorbed layer. For this reason, contradictory conclusions may be drawn. A new thermodynamic approach which is free from the above shortcoming is described. In particular, if is shown that all the adsorption parameters, including that of size ratio, can be obtained on the basis of purely thermodynamic arguments without any reference to molecular models. Thus, the popular Frumkin and Bennes isotherms are proved to be valueless. It is also shown that useful information about the adsorption process and the interfacial interactions can be gained only when the adsorption parameters are interpreted by means of up-to-date molecular models for charged interfaces. The field effect and the physical content of the various adsorption parameters are examined. Finally, an analysis of the accuracy of the experimental data needed for the complete application of the new thennodynamic approach is also presented and discussed.

Modeling the combined effect of temperature and organic modifier content on reversed-phase chromatographic retention - Effectiveness of derived models in isocratic and isothermal mode retention prediction

Models considering simultaneously mobile phase organic content and column temperature were developed in this study by an extension of different equations describing the influence of temperature on solute retention. This extension was achieved by two methods: a semi-thermodynamic and a direct combination of equations expressed separately the dependence of the retention upon each of these factors. The above approaches gave a great number of expressions for the logarithm of the solute retention factor in terms of both temperature and organic content in the mobile phase, ln k(T,phi), determined from the dependence of the standard enthalpy of the retention process on T. From the final expressions of ln k(T,phi) we tested only those with the minimum number of adjustable parameters, i.e. those that correspond to a constant standard enthalpy of the retention process. For this test we examined the retention behaviour of a sample of alkylbenzenes in aqueous acetonitrile eluents. These compounds exhibit ln k versus 1/T plots with a very small curvature. We found that a new equation for ln k(T,phi) based on the adsorption model for retention performs better than all the others. The average percentage prediction error ranges from 0.7 to 1.4%.

On the use of genetic algorithms for response surface modeling in high-performance liquid chromatography and their combination with the Microsoft Solver

Four genetic algorithms--the classical, Haupts, Brunettis and a modification of the classical algorithm suggested in the present paper--are examined when they are used for the modeling of response surfaces in high-performance liquid chromatography (HPLC). We found that the best results are obtained from our modification and the worst by Haupts algorithm. The classical genetic algorithm gives satisfactory results, better than those of Brunettis algorithm. We also ascertained that all genetic algorithms may get stuck in a local minimum other than the global one, except for our modification, which can be considered to approach a global method. Finally, the time needed for the optimization of a genetic algorithm and the combination of a genetic algorithm with a non-linear least-squares routine are considered and discussed.

New equations describing the combined effect of pH and organic modifier concentration on the retention in reversed-phase liquid chromatography

Six equations that express the combined effect of mobile phase pH and organic modifier content on sample retention in reversed-phase liquid chromatography (RPLC) are developed based on either the adsorption or the partition model for retention. The equations are tested against five retention data sets taken from literature. In the tests two pH scales are used, w(w)pH and s(s)pH. It is shown that a new seven-parameter equation works more satisfactorily, because it exhibits good numerical behavior, gives low values of the sum of squares of residuals and represents the experimental retention surfaces successfully. In addition, the danger of overfitting, which leads to the prediction of physically meaningless retention surfaces, is minimized by using the proposed new seven-parameter equation. Finally, the possibility of obtaining reliable pK values of weak acids or bases chromatographically by means of the derived equations is also considered and discussed.

Interfacial micellization of cetyl-dimethyl-benzylammonium chloride and Tween-80R at the Hg/electrolyte solution interphase

Abstract The adsorption of a cationic micelle—forming surfactant, cetyl—dimethyl-benzylammonium chloride, and of a neutral surfactant, Tween 80 R , from aqueous electrolyte solutions on a polarized mercury electrode was studied by means of differential capacitance measurements in order to examine the influence of the structure and charge of the adsorbate on interfacial micellization. For both surfactants, deformed capacitance peaks were recorded, accompanied by capacitance plateaux. These are sufficient criteria for the occurrence of a two- or three-dimensional aggregation process of the adsorbate molecules within the electrical double layer. The adsorption behaviour of cetyl-dimethyl-benzylammonium cations shows striking similarities with that of sodium dodecylsulphate. Their aggregates on the electrode surface collapse to a compact layer at potentials negative of the ecm and a polylayer is formed under favourable conditions at far negative or positive polarizations respectively. Since these adsorbates have quite different structures, these similarities are attributed to their ionic character. In contrast, the surface aggregates of Tween 80 R do not collapse to a compact layer but are stable over an extended potential range, forming two micellar plateaux. Finally, general conclusions of our theoretical and experimental studies on micellization at charged interphases are also presented.

New Approaches to Linear Gradient Elution Used for Optimization in Reversed-Phase Liquid Chromatography

Abstract The various approaches developed for prediction and optimization in linear gradient elution in reversed-phase liquid chromatography are critically reviewed. These approaches concern both single-mode and multi-mode gradient elution, the latter involving either gradients related exclusively to the mobile phase composition or combined gradients of the mobile phase composition with flow rate and/or column temperature or combined gradients of flow rate and column temperature. The advantages and disadvantages of each method are discussed and special attention is devoted to the factors that affect the quality of the prediction and their impact to the optimisation. Finally, the fitting techniques and optimisation methods adopted in linear gradient elution are presented and the most effective algorithms used for this purpose are indicated and discussed.

Simple models for adsorption on electrodes: I. Adsorption of monomeric neutral organic molecules

Abstract Simple molecular models are developed to describe the single adsorption of monomer neutral organic compounds and the reorientation and coadsorption processes of these substances on ideally polarized electrodes. The equilibrium properties are determined within the framework of lattice statistics using the mean field approximation under the assumption of a mean electrical field acting at each site. Neglecting short-range interactions, the first model for single adsorption predicts langmuirian adsorption isotherms, which are congruent only with respect to potential, and a quadratic dependence of the Gibbs energy of adsorption on the potential. The model was tested by comparison with a variety of experimental data and satisfactory agreement was found over a wide range of adsorbate concentrations and polarizations, even in cases where the experimental data exhibit deviations from langmuirian behaviour. Generalizations of this model to include short-range interactions, variations of the adsorbed layer thickness and changes in the state of the solvent molecules are examined. The model for reorientation and coadsorption processes is also an extension of the first model. Comparisons of its predictions with experimental data show that it describes almost quantitatively all the experimental features observed during a reorientation process of an organic adsorbate when it exhibits two distinct polarization states on a mercury electrode. Moreover, it can provide a satisfactory description of the coadsorption of two organic adsorbates, without using additional adjustable parameters, but from the known properties of their single adsorption. Thus, the models developed in this paper combine both simplicity and applicability and therefore they can be used to analyse a variety of experimental adsorption data.

Adsorption of sodium dodecylsulphate on mercury as an example of micellization within a multilayer interphase

Abstract The adsorption of sodium dodecylsulphate from aqueous electrolytic solutions on a polarized mercury electrode was studied by means of differential capacitance measurements over a wide range of concentration and potential, and in the presence of different supporting electrolytes with different ionic strengths. An interpretation of the differential capacitance vs. applied potential curves is given, based on theoretical treatments developed previously. It is shown that at concentrations below the cmc, two-dimensional aggregates are formed on the electrode surface within a polarization region which is bounded by two capacitance peaks at extreme positive and negative polarizations. This film is not particularly stable and is transformed into a compact layer at polarizations close to the potential of maximum adsorption, resulting in a capacitance pit. With increasing bulk concentration the aggregation process extends across the interphase and at least two layers of aggregates—micelles are formed at concentrations around and above the cmc. This three-dimensional aggregation is characterized by the appearance of deformed and/or split capacitance peaks which determine the polarization region where this phenomenon occurs.