Sarah C. Rutan

Resolution of multicomponent overlapped peaks by the orthogonal projection approach, evolving factor analysis and window factor analysis

Abstract The orthogonal projection approach (OPA), a stepwise approach developed for the determination of the number of compounds present in a multicomponent system, has been extended by including a step that allows the chromatographic and spectroscopic pure compound profiles to be determined. This is done using an alternating least-squares procedure. The initial estimations are the spectra selected in the first step of OPA. The performance of the OPA algorithm is compared with that of two window-based self-modelling curve resolution approaches: evolving factor analysis (EFA) and window factor analysis (WFA).

Comparative Study of Hydrocarbon, Fluorocarbon, and Aromatic Bonded RP-HPLC Stationary Phases by Linear Solvation Energy Relationships

The retention properties of eight alkyl, aromatic, and fluorinated reversed-phase high-performance liquid chromatography bonded phases were characterized through the use of linear solvation energy relationships (LSERs). The stationary phases were investigated in a series of methanol/water mobile phases. USER results show that solute molecular size and hydrogen bond acceptor basicity under all conditions are the two dominant retention controlling factors and that these two factors are linearly correlated when either different stationary phases at a fixed mobile-phase composition or different mobile-phase compositions at a fixed stationary phase are considered. The large variation in the dependence of retention on solute molecular volume as only the stationary phase is changed indicates that the dispersive interactions between nonpolar solutes and the stationary phase are quite significant relative to the energy of the mobile-phase cavity formation process. PCA results indicate that one PCA factor is required to explain the data when stationary phases of the same chemical nature (alkyl, aromatic, and fluoroalkyl phases) are individually considered. However, three PCA factors are not quite sufficient to explain the whole data set for the three classes of stationary phases. Despite this, the average standard deviation obtained by the use of these principal component factors are significantly smaller than the average standard deviation obtained by the USER approach. In addition, selectivities predicted through the USER equation are not in complete agreement with experimental results. These results show that the LSER model does not properly account for all molecular interactions involved in RP-HPLC. The failure could reside in the V 2 solute parameter used to account for both dispersive and cohesive interactions since shape selectivity predictions for a pair of structural isomers are very bad.

Solvatochromically based solvent-selectivity triangle

Abstract A classification of common solvents according to their dipolarity and hydrogen-bonding acidity and basicity has been developed, based on the Kamlet—Taft solvatochromic parameter scheme. This approach has been compared with the Snyder—Rohrschneider solvent-selectivity triangle (SST). The two solvent-classification schemes are found to be generally similar. Both SST-based schemes are also compared to an analysis of solvent selectivity based on linear salvation energy relationships. While there are considerable similarities, important practical differences, especially in the case of reversed-phase liquid chromatography, are evident.

Comparison between the direct trilinear decomposition and the multivariate curve resolution-alternating least squares methods for the resolution of three-way data sets

Abstract Direct trilinear decomposition (DTD) and multivariate curve resolution-alternating least squares (MCR-ALS) methods are two of the most representative three-way resolution procedures. The former, non-iterative, is based on the resolution of the generalized eigenvector/eigenvalue problem and the latter, iterative, is focused on the optimization of initial estimates by using data structure and chemical constraints. DTD and MCR-ALS have been tested on a variety of three-way simulated data sets having common sources of variation in real response profiles, such as signal shift, broadening or shape distortions caused by noise. The effect of these factors on the resolution results has been evaluated through the analysis of several parameters related to the recovery of both qualitative and quantitative information and to the quality of the overall data description. Conclusions inferred from the simulated examples help to clarify the performance of both methods on a real example and to provide some general guidelines to understand better the potential of each method.

MULTIVARIATE PEAK PURITY APPROACHES

Abstract The mathematical basis and interpretation of the results of several multivariate techniques for the determination of the number of compounds present in an evolving multicomponent system are presented. All the techniques described are applicable to bilinear data matrices obtained from evolutionary processes, i.e., the concentration of each compound evolves with an ordered variable such as time or pH. Their performance for the detection of a minor compound in the presence of a main one is discussed. The application to systems with more than 2 compounds and the effect of smoothing are also considered.

Multivariate curve resolution with non-linear fitting of kinetic profiles

Abstract This paper describes the incorporation of a hard modeling step based on a kinetic model, into a soft modeling (multivariate curve resolution) technique. The soft modeling technique allows for the determination of the retention and spectral profiles from overlapped components while the hard modeling step allows for the simultaneous prediction of the rate constants of the various steps in the reaction pathway. The program uses standard MATLAB® functions for determining the solutions of the differential equations as well as for finding the optimal rate constants to describe the kinetic profiles. The kinetic model is entered by a set of command line parameters and can describe any order chemical reaction with multiple reaction pathways. This paper uses simulated first- and second-order reaction data as well as real data to characterize the performance of the program. The algorithm is able to resolve overlapped retention and spectral profiles and predict the rate constants for the reaction.

Adaptive Kalman filtering used to compensate for model errors in multicomponent methods

Abstract An adaptive Kalman filtering technique is developed and evaluated as a tool for compensation of model errors that commonly occur in multicomponent problems. Results presented demonstrate that the adaptive Kalman filter should be of considerable value for obtaining accurate concentrations and spectral information from multicomponent responses. The restrictions of the technique are that the model must be correct for a portion of the response, and the errors must be attributable to a single component. Concentration estimates are accurate for those components which are modeled correctly, but the concentration estimate obtained for the component not included in the model may not always be reliable. The technique is evaluated for multicomponent problems in spectroscopy and voltammetry.

Background subtraction for fluorescence detection in thin-layer chromatography with derivative spectrometry and the adaptive Kalman filter

Abstract Background signals must be removed from analyte responses before reliable qualitative and quantitative results can be obtained. For cases in which a reliable estimate for the background response cannot be obtained, the combination of two mathematical approaches yields accurate quantitative results. First-derivative spectrometric methods, in conjunction with a curve-resolution approach based on the adaptive Kalman filter, are used to compensate for difficulties caused by background responses which are not reproducible. Derivative spectrometric techniques reduce the relative magnitude of low-frequency systematic deviations in the spectra. In this case, this has the effect of localizing model errors to restricted regions of the spectra, which in turn meets the major requirement for successful utilization of the adaptive Kalman filter. The approach is applied to fluorimetric detection for thin-layer chromatography in the quantification of polynuclear atomatic hydrocarbon compounds. Results are given which demonstrate that this combined approach yields accurate estimates for concentrations of components in overlapped chromatographic zones. A derivative spectrometric approach in conjunction with a regular Kalman-filter fit gives less accurate results, and an adaptive Kalman filter used to fit the raw spectral data fails to give any reliable quantitative information. The combined approach using derivative spectrometry anal the adaptive Kalman filter is shown to give 8-fold lower detection limits for anthracene when compared to traditional background-subtraction methods.

Estimation of first-order kinetic parameters by using the extended kalman filter

Abstract A model for first-order kinetics is derived for spectra obtained while a reaction is taking place. A technique for nonlinear-regression analysis known as the extended Kalman filter is used to estimate the initial concentrations of the reactants and the rate constant from the spectral data. The effects of the magnitude of the rate constant and the identity of the absorbing species are examined for synthetic spectra containing overlapped responses. The technique is used successfully to obtain the rate constant for the dissociation reaction of a praseodymium complex. The filter is also shown to be useful for the detection of erros in the kinetic model employed to fit the data. The extended Kalman filter can be used to fit kinetic models other than the one discussed here, and may prove to be a valuable technique for estimation of kinetic parameters.

Electronic spectroscopic investigations of the stationary phase in reversed-phase liquid chromatography

Abstract Electronic spectroscopy of probe molecules provides a powerful means of characterizing the stationary phase in reversed-phase liquid chromatography. In particular, both fluorescence and UV—visible absorption spectroscopies have been used to characterize these complex interfacial environments. This article reviews the progress made with these approaches for studying the structure of the stationary phase, the solute environment that it produces, and the dynamics of sorbed molecules in reversed-phase liquid chromatography. Fluorescence studies using either covalently attached probes, or physiosorbed probes are reviewed, along with total internal reflection fluorescence studies of flat, model interfaces. Dynamic effects due to excimer formation and quenching are shown to provide information about hydrocarbon ligand proximity, microviscosity, and contact of sorbed molecules with the mobile phase. UV—visible diffuse reflectance spectroscopy has also been used to characterize the dipolarity, polarizability and hydrogen bonding interactions of the reversed-phase surface environment. These electronic spectroscopic approaches lend insight into the organization, orientation, and polarity of the alkyl chains. In this article, the results of these studies are reviewed, and their impact on models for reversed- phase retention are discussed.