On the ambiguity of the reaction rate constants in multivariate curve resolution for reversible first-order reaction systems

Multivariate curve resolution for kinetic modeling and scale-up prediction

Abstract

An imine synthesis was investigated in a nearly isothermal oscillating segmented flow microreactor at different temperatures using non-invasive Raman spectroscopy. Multivariate curve resolution provided a calibration-free approach for obtaining kinetic parameters. The two different multivariate curve resolution approaches, soft and hard modeling, were applied and contrasted, leading to similar results. Taking heat and mass balance into account, the proposed kinetic model was applied for a model-based scale-up prediction. Finally, the reaction was performed in a 0.5 L semi-batch reactor, followed by in-line Raman spectroscopy and off-line gas chromatography analysis. The successful scale-up was demonstrated with a good agreement between measured and predicted concentration profiles.

Highlights

• Oscillation segmented flow reactor with inline Raman spectroscopy.

• Multivariate Curve Resolution with hard and soft constraints.

• High quality kinetic model for scale-up predictions.

Graphical abstract

A multi-method chemometric analysis in spectroelectrochemistry: Case study on molybdenum mono-dithiolene complexes

Spectroelectrochemical (SEC) analyses combine spectroscopic measurements with electrochemical techniques and can provide deep insight into complex multi-component chemical reaction systems. SEC experiments typically produce large amounts of spectroscopic data. Chemometric techniques are required for the data analysis and aim at extracting the underlying pure component information. Here we analyze spectroelectrochemically gained UV-vis data from five molybdenum mono-dithiolene complexes with changing redox states. SEC enables an electrochemical control of the mixture composition which supports the application of chemometric curve resolution techniques. The factor ambiguity problem is addressed by a multi-method approach combining chemometric tools from the evolving factor analysis (EFA) and from the area of feasible solutions (AFS) methodology in combination with factor duality arguments. EFA enables a subsystem analysis. Two subsystems with three species each are identified, which belong to a reductive and to an oxidative region. A joint species is contained in both regions. A complete pure component decomposition becomes possible in a final step.

Reaction rate ambiguities for perturbed spectroscopic data: Theory and implementation

The analysis of reaction systems and their kinetic modeling is important for both exploratory research and process design. Multivariate curve resolution (MCR) methods are state-of-the-art tools for the analysis of spectral series, but are also affected by an unavoidable solution ambiguity that impacts the obtained concentration profiles, spectra and model parameters. These uncertainties depend on the underlying model and the magnitude of the measurement perturbations. We present a general theoretical approach together with a computational method for the analysis of the solution ambiguity underlying arbitrary kinetic models. The main idea is to determine all those model parameters for which the corresponding pure component factorizations satisfy all given constraints within small error tolerances. This makes it possible to determine bands of concentration profiles and spectra that reflect the underlying ambiguity and circumscribes the potential reliability of MCR solutions. False conclusions on the uniqueness of a solution can be prevented. The procedure can be applied as a post-processing step to MCR methods as MCR-ALS, ReactLab or others. The Matlab program code is freely accessible and includes not only the proposed ambiguity analysis but also an MCR hard-modeling approach. Application studies are presented for two experimental data sets, namely for UV/Vis spectra on the relaxation of a photoexcited state of benzophenone and for Raman spectra on an aldehyde formation process.

On the analysis of chromatographic biopharmaceutical data by curve resolution techniques in the framework of the area of feasible solutions

Monitoring preparative protein chromatographic steps by in-line spectroscopic tools or fraction analytics results in medium or large sized data matrices. Multivariate Curve Resolution (MCR) serve to compute or to estimate the concentration values of the pure components only from these data matrices. However, MCR methods often suffer from an inherent solution ambiguity which underlies the factorization problem. The typical unimodality of the chromatographic profiles of pure components can support the chemometric analysis. Here we present the pure components estimation process within the framework of the area of feasible solutions, which is a systematic approach to represent the range of all possible solutions. The unimodality constraint in combination with Pareto optimization is shown to be an effective method for the pure component calculation. Applications are presented for chromatograms on a model protein mixture containing ribonuclease A, cytochrome c and lysozyme and on a two-dimensional chromatographic separation of a monoclonal antibody from its aggregate species. The root mean squared errors of the first case study are 0.0373, 0.0529 and 0.0380 g/L compared to traditional off-line analytics. The second case study illustrates the potential of recovering hidden components with MCR from off-line reference analytics.

Facile Synthesis of a Stable Side-on Phosphinyne Complex by Redox Driven Intramolecular Cyclisation

Alkyne complexes with vicinal substitution by a Lewis acid and a Lewis base at the coordinated alkyne are prospective frustrated Lewis pairs exhibiting a particular mutual distance and, hence, a specific activation potential. In this contribution, investigations on the generation of a WII alkyne complex bearing a phosphine as Lewis base and a carbenium group as Lewis acid are presented. Independently on potential substrates added, an intramolecular cyclisation product was always isolated. A subsequent deprotonation step led to an unprecedented side-on λ5 -phosphinyne complex, which is interpreted as highly zwitterionic according to visible absorption spectroscopy supported by TD-DFT. Low-temperature 31 P NMR and EPR spectroscopic measurements combined with time-dependent IR-spectroscopic monitoring provided insights in the mechanism of the cyclisation reaction. Decomposition of the multicomponent IR spectra by multivariate curve resolution and a kinetic hard-modelling approach allowed the derivation of kinetic parameters. Assignment of the individual IR spectra to potential intermediates was provided by DFT calculations.

Photochemical multivariate curve resolution models for the investigation of photochromic systems under continuous irradiation

We propose a multivariate curve resolution approach for the investigation of photochromic systems using UV-Visible spectroscopy. The incorporation of photochemical hard-models as constraints in multivariate curve resolution alternating least squares (MCR-ALS) allows extracting reaction quantum yields in situations where a complete knowledge of the system is not available. We apply this approach to the study of the photochromism of CMTE (cis-1,2-dicyano-1,2-bis(2,4,5-trimethyl-3-thienyl)ethene) under continuous monochromatic irradiation. The mechanism, involving 3 species and 2 reversible reactions, is written and translated into a kinetic constraint that can be applied to the concentration profiles within ALS. First, ambiguity of the solution obtained for photochemical model(s) is calculated and discussed for single set analysis. Multiset analysis is then proposed combining data obtained under different irradiation wavelengths to provide more reliable results. Finally, the photochemical reactivity of CMTE is widely unraveled, and some description of the mechanism observed under irradiation at 365 nm is given.

A chemometric study in the area of feasible solution of an acid–base titration of N-methyl-6-oxyquinolone

Multivariate curve resolution methods aim at recovering the underlying chemical components from spectroscopic data on chemical reaction systems. In most cases the spectra and concentration profiles of the pure components cannot be uniquely determined from the given spectral data. Instead continua of possible factors exist. This fact is known as rotational ambiguity. The sets of all possible pure component factors can be represented in the so-called area of feasible solutions (AFS). This paper presents an AFS study of the pure component reconstruction problem for a series of UV/Vis spectra taken from an acid–base titration of N-methyl-6-oxyquinolone. Additional information on the equilibrium concentration profiles for a varying acid concentration is taken from fluorescence measurements. On this basis chemometric duality arguments lead to the construction of a unique final solution.

Multivariate curve resolution methods aim at recovering the underlying chemical components from spectroscopic data on chemical reaction systems.