Mathias Sawall

Exploring Between the Extremes: Conversion‐Dependent Kinetics of Phosphite‐Modified Hydroformylation Catalysis

The kinetics of the hydroformylation of 3,3-dimethyl-1-butene with a rhodium monophosphite catalyst has been studied in detail. Time-dependent concentration profiles covering the entire olefin conversion range were derived from in situ high-pressure FTIR spectroscopic data for both, pure organic components and catalytic intermediates. These profiles fit to Michaelis-Menten-type kinetics with competitive and uncompetitive side reactions involved. The characteristics found for the influence of the hydrogen concentration verify that the pre-equilibrium towards the catalyst substrate complex is not established. It has been proven experimentally that the hydrogenolysis of the intermediate acyl complex remains rate limiting even at high conversions when the rhodium hydride is the predominant resting state and the reaction is nearly of first order with respect to the olefin. Results from in situ FTIR and high-pressure (HP) NMR spectroscopy and from DFT calculations support the coordination of only one phosphite ligand in the dominating intermediates and a preferred axial position of the phosphite in the electronically saturated, trigonal bipyramidal (tbp)-structured acyl rhodium complex.

A fast polygon inflation algorithm to compute the area of feasible solutions for three-component systems. I: concepts and applications

The multicomponent factorization of multivariate data often results in nonunique solutions. The so‐called rotational ambiguity paraphrases the existence of multiple solutions that can be represented by the area of feasible solutions (AFS). The AFS is a bounded set that may consist of isolated subsets. The numerical computation of the AFS is well understood for two‐component systems and is an expensive numerical process for three‐component systems. In this paper, a new fast and accurate algorithm is suggested that is based on the inflation of polygons. Starting with an initial triangle located in a topologically connected subset of the AFS, an automatic extrusion algorithm is used to form a sequence of growing polygons that approximate the AFS from the interior. The polygon inflation algorithm can be generalized to systems with more than three components. The efficiency of this algorithm is demonstrated for a model problem including noise and a multicomponent chemical reaction system. Further, the method is compared with the recent triangle‐boundary‐enclosing scheme of Golshan, Abdollahi, and Maeder (Anal. Chem. 2011, 83, 836–841). Copyright

Reduction of the rotational ambiguity of curve resolution techniques under partial knowledge of the factors. Complementarity and coupling theorems

Multivariate curve resolution techniques allow to uncover from a series of spectra (of a chemical reaction system) the underlying spectra of the pure components and the associated concentration profiles along the time axis. Usually, a range of feasible solutions exists because of the so‐called rotational ambiguity. Any additional information on the system should be utilized to reduce this ambiguity.

A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.

A Comparative In Situ HP-FTIR Spectroscopic Study of Bi- and Monodentate Phosphite-Modified Hydroformylation

The rhodium‐catalyzed phosphite‐modified hydroformylation of 3,3‐dimethyl‐1‐butene is comparatively studied for a bidentate and a monodentate phosphite using in situ high‐pressure (HP) FTIR spectroscopy and GC analysis. With the bidentate ligand at 70 °C, a pseudo‐first‐order reaction with respect to the olefin takes place, with the pentacoordinate hydrido complex being the only detectable intermediate during the reaction. In contrast, for the monodentate ligand, a zeroth‐ to pseudo‐first‐order shift is characteristic with the major intermediate for this system subsequently changing from the coordinatively saturated acyl complex to the respective hydrido complex already at low conversions. Application of the PCD (pure component decomposition) algorithm to the reaction spectra affords the concentration versus time profiles of these intermediates, providing proof that the reaction rate remains controlled by rhodium acyl hydrogenolysis even at medium to high olefin conversions when the corresponding hydrido complex is the major organometallic component. If the reaction is carried out at a temperature of 30 °C in neat olefin, results from both GC and HP‐FTIR verify an intermediate regime of saturation kinetics and also the presence of an acyl complex at low olefin conversions for the diphosphite. Initial turnover frequencies of 237 h−1 and 1040 h−1 are obtained for the mono‐ and the diphosphite, respectively, at 30 °C, which implies an intrinsically faster hydrogenolysis of the diphosphite‐derived acyl rhodium complex at this low temperature.

A fast polygon inflation algorithm to compute the area of feasible solutions for three-component systems. II: Theoretical foundation, inverse polygon inflation, and FAC-PACK implementation

The area of feasible solutions (AFS) of a multivariate curve resolution method is the continuum of feasible solutions under the given constraints. In the current paper, the AFS is computed only on the condition of nonnegative solutions. This work is a continuation of a paper (J. Chemometrics 28:106–116, 2013) on the polygon inflation algorithm for AFS computations. In this second part, various properties of the AFS are analyzed. First, its boundedness is proved, which is a necessary condition for its numerical computation. Second, it is shown that the origin is never contained in the area of feasible solutions. This fact is the basis for the inverse polygon inflation algorithm, which allows to compute specific types of an AFS containing a hole.

Model-free multivariate curve resolution combined with model-based kinetics: algorithm and applications

Multivariate curve resolution techniques are powerful tools to extract from sequences of spectra of a chemical reaction system the number of independent chemical components, their associated spectra, and the concentration profiles in time. Usually, these solutions are not unique because of the so‐called rotational ambiguity.

On the area of feasible solutions and its reduction by the complementarity theorem

Multivariate curve resolution techniques in chemometrics allow to uncover the pure component information of mixed spectroscopic data. However, the so-called rotational ambiguity is a difficult hurdle in solving this factorization problem. The aim of this paper is to combine two powerful methodological approaches in order to solve the factorization problem successfully. The first approach is the simultaneous representation of all feasible nonnegative solutions in the area of feasible solutions (AFS) and the second approach is the complementarity theorem. This theorem allows to formulate serious restrictions on the factors under partial knowledge of certain pure component spectra or pure component concentration profiles. In this paper the mathematical background of the AFS and of the complementarity theorem is introduced, their mathematical connection is analyzed and the results are applied to spectroscopic data. We consider a three-component reaction subsystem of the Rhodium-catalyzed hydroformylation process and a four-component model problem.

On generalized Borgen plots. I: From convex to affine combinations and applications to spectral dataSpectra†

In 1985, Borgen and Kowalski (Anal. Chim. Acta 1985; 174: 1‐26) published their landmark paper on the geometric construction of feasible regions for nonnegative factorizations of spectral data matrices for three‐component systems. These geometric constructions are called Borgen plots. Borgen plots are principally restricted to nonnegative data and are sometimes considered as analytical tool. Major contributions to this theory have been given by Rajkó. In contrast to these geometric constructions, numerical methods to compute the so‐called area of feasible solutions (AFS) have been studied by Golshan et al. (Anal. Chem. 2011; 83 (3): 836‐841) and by Sawall et al. (J. Chemom. 2013; 27: 106‐116). These numerical methods can even treat spectral data, which include slightly negative components.

An Operando FTIR Spectroscopic and Kinetic Study of Carbon Monoxide Pressure Influence on Rhodium-Catalyzed Olefin Hydroformylation

The influence of carbon monoxide concentration on the kinetics of the hydroformylation of 3,3-dimethyl-1-butene with a phosphite-modified rhodium catalyst has been studied for the pressure range p(CO)=0.20-3.83 MPa. Highly resolved time-dependent concentration profiles of the organometallic intermediates were derived from IR spectroscopic data collected in situ for the entire olefin-conversion range. The dynamics of the catalyst and organic components are described by enzyme-type kinetics with competitive and uncompetitive inhibition reactions involving carbon monoxide taken into account. Saturation of the alkyl-rhodium intermediates with carbon monoxide as a cosubstrate occurs between 1.5 and 2 MPa of carbon monoxide pressure, which brings about a convergence of aldehyde regioselectivity. Hydrogenolysis of the acyl intermediate is fast at 30 °C and low pressure of p(CO)=0.2 MPa, but is of minus first order with respect to the solution concentration of carbon monoxide. Resting 18-electron hydrido and acyl complexes that correspond to early and late rate-determining states, respectively, coexist as long as the conversion of the substrate is not complete.