Marcel Maeder

Calculation of equilibrium constants from multiwavelength spectroscopic data-I Mathematical considerations.

Multiwavelength spectrophotometric and spectroscopic data in general contain considerably more information about complexation equilibria than potentiometric data do. With the construction of a fully automatic titration set-up built into a high-precision spectrophotometer, the problems related to the wider use of this method have shifted from the quality of the primary data to the complexity of their numerical treatment. Matrix algebra is used to show how these problems can be overcome. An algorithm is described for calculation of stability constants and absorption spectra, together with the associated standard errors, at a reasonable expense of computer time. Problems in finding the minimum in a multidimensional parameter space are reduced by elimination of the molar absorptivities from the algorithm for the iterative refinement. Numerical safety and speed of calculation are improved by use of analytical instead of numerical derivatives. The number of data to be fitted is decreased by principal-component analysis.

Calculation of equilibrium constants from multiwavelength spectroscopic data--II: SPECFIT: two user-friendly programs in basic and standard FORTRAN 77.

A new program (SPECFIT), written in HP BASIC or FORTRAN 77, for the calculation of stability constants from spectroscopic data, is presented. Stability constants have been successfully calculated from multiwavelength spectrophotometric and EPR data, but the program can be equally well applied to the numerical treatment of other spectroscopic measurements. The special features included in SPECFIT to improve convergence, increase numerical reliability, and minimize memory as well as computing time requirements, include (i) elimination of the linear parameters (i.e., molar absorptivities), (ii) the use of analytical instead of numerical derivatives and (iii) factor analysis. Calculation of stability constants from spectroscopic data is then as straightforward as from potentiometric titration curves and gives results of analogous reproducibility. The spectroscopic method has proved, however, to be superior in discrimination between chemical models.

Combining hard- and soft-modelling to solve kinetic problems

Abstract A novel approach mixing the qualities of hard-modelling and soft-modelling methods is proposed to analyse kinetic data monitored spectrometrically. Taking as a basis the Multivariate Curve Resolution–Alternating Least Squares method (MCR–ALS), which obtains the pure concentration profiles and spectra of all absorbing species present in the raw measurements by using typical soft-modelling constraints, a new hard constraint is introduced to force some or all the concentration profiles to fulfill a kinetic model, which is refined at each iterative cycle of the optimisation process. This modification of MCR–ALS drastically decreases the rotational ambiguity associated with the kinetic profiles obtained using exclusively soft-modelling constraints. The optional inclusion of some or all the absorbing species into the kinetic model allows the successful treatment of data matrices whose instrumental response is not exclusively due to the chemical components involved in the kinetic process, an impossible scenario for classical hard-modelling approaches. Moreover, the possible distinct constraint of each of the matrices in a three-way data set allows for the simultaneous analysis of kinetic runs with diverse kinetic models and rate constants. Thus, the introduction of model-based and model-free features in the treatment of kinetic data sets yields more satisfactory results than the application of pure hard- or pure soft-modelling approaches. Simulated and real examples are used to confirm this statement.

The resolution of overlapping chromatographic peaks by evolving factor analysis

Abstract A completely model-free method for the resolution of overlapping chromatographic peaks is presented. Evolving factor analysis enhances the power of classical factor analysis by exploiting the additional information contained in the response data through the intrinsic order of the elution time. The results are the elution profiles and the normalized spectra of the components.

Evolving factor analysis, a new multivariate technique in chromatography

Abstract Overlapping peaks are a general problem in chromatography. Modern multichannel detectors such as the diode-array detector allow multivariate techniques for a computational resolution. Evolving factor analysis (EFA) is a recently developed method for a completely model-free resolution of overlapping peaks into concentration profiles and absorption spectra. EFA is successfully tested with real chromatograms. The requirements concerning the quality of the measured data are discussed and related to the scope and fields of application of EFA.

Spectroscopic imaging and chemometrics: a powerful combination for global and local sample analysis

Merging spectroscopic imaging and chemometrics enhances the outcomes of instrumental technology and data analysis. Multivariate exploratory and resolution methods can be adapted to image analysis and provide global and local information about pure compounds in an imaged sample. Knowing in detail how the chemical compounds are distributed over the scanned surface gives valuable information about essential issues in the manufacture and the characterization of products, such as evenness of composition and, therefore, homogeneity of the sample. The power to detect and to locate impurities is also greatly enhanced because these unwanted compounds could show locally large concentrations (and signals), even though their abundance on the surface is very low. The capabilities of this combination are shown in an example of pharmaceutical product control, where analysis of the end product requires chemical characterization and quantitative information at global and local levels. The approach used and the kind of information obtained is general and can be applied to the analysis of images in other fields.

Kinetics and Mechanism of Carbamate Formation from CO2(aq), Carbonate Species, and Monoethanolamine in Aqueous Solution

Removal of carbon dioxide from fossil-based power generation is a potentially useful technique for the reduction of greenhouse gas emissions. Reversible interaction with aqueous amine solutions is most promising. In this process, the formation of carbamates is an important reaction of carbon dioxide. In this contribution, a detailed molecular reaction mechanism for the carbamate formation between MEA (monoethanolamine) and dissolved CO(2) as well as carbonate species in aqueous solution is presented. There are three parallel, reversible reactions of the free amine with CO(2), carbonic acid, and the bicarbonate ion; the relative importance of the three paths is strongly pH dependent. Kinetic and equilibrium measurements are based on (1)H NMR and stopped-flow measurements with rate constants, equilibrium constants, and protonation constants being reported.

Comprehensive Study of the Hydration and Dehydration Reactions of Carbon Dioxide in Aqueous Solution

The reversible interactions of dissolved CO(2) with H(2)O and OH(-) to form H(2)CO(3) and HCO(3)(-) in aqueous solution have been investigated using spectrophotometric stopped-flow measurements. The progress of the reactions was monitored via indicators coupled to the pH changes during the reactions. The study, involving global analysis of the complete data set, spanned the temperature range 6.6-42.8 degrees C and resulted in the evaluation of all rate and equilibrium constants as well as activation parameters for the kinetic data and the reaction enthalpies and entropies for the equilibrium constants.

Quantification of a known component in an unknown mixture

Abstract A method is described for quantifying individual absorbing species in mixtures of unknown composition. The algorithm can be applied to the resolution of chromatographic peaks, to the evaluation of spectrophotmetric titrations, and to related methods producing ordered, two-dimensional arrays of data. In contrast to rank-annihilation factor analysis, it is sufficient to know the absorption spectrum of the species in question. All information about the response in the second dimension, e.g., the concentration profile(s), results from the numerical analysis.

Second order global analysis: the evaluation of series of spectrophotometric titrations for improved determination of equilibrium constants

Abstract In spectrophotometric titrations, linear or near-linear dependence of concentration profiles and the existence of minor species cause difficulties in the evaluation of the data. In the first case calculated absorption spectra and in the second case the corresponding equilibrium constants are not or only poorly defined. The result is the inability to reliably fit a reasonable model to the data. In second order global analysis, a number of spectrophotometric titrations with different initial concentrations are simultaneously analysed. In this way the concentration matrix is augmented to full rank and, secondly, conditions for the significant formation of each species can be obtained. Resulting equilibrium constants and absorption spectra are notably better defined. EQUISPEC is a computer program using the matrix based MATLAB environment for second order global analysis of spectrophotometric equilibrium data. It has been successfully tested with generated data and shown to overcome linear dependence and reproduce reported stability constants for the zinc: 1,10-phenanthroline system and to considerably improve the analysis of the complexation of Cu 2+ by diethylenetriamine (dien).