Construction of a Lyapunov functional for a class of controlled population balance models

In this paper, we consider a class of controlled population balance equations describing granulation processes in chemical engineering. Such a control system admits an equilibrium which is not asymptotically stable in general. In order to stabilize this equilibrium, we consider the perturbed system and introduce a Lyapunov functional candidate as a weighted L²-norm. It is shown that the weight function for this construction may be defined in terms of solutions to a certain differential inequality. We present a solution of this differential inequality in a particular case and discuss possible extensions of this approach for multidimensional hyperbolic systems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ball milling in organic synthesis: solutions and challenges

During the last decade numerous protocols have been published using the method of ball milling for synthesis all over the field of organic chemistry. However, compared to other methods leaving their marks on the road to sustainable synthesis (e.g. microwave, ultrasound, ionic liquids) chemistry in ball mills is rather underrepresented in the knowledge of organic chemists. Especially, in the last three years the interest in this technique raised continuously, culminating in several high-quality synthetic procedures covering the whole range of organic synthesis. Thus, the present tutorial review will be focused on the highlights using this method of energy transfer and energy dissipation. The central aim is to motivate researchers to take notice of ball mills as chemical reactors, implementing this technique in everyday laboratory use and thus, pave the ground for future activities in this interdisciplinary field of research.     

Stitching phospholanes together piece by piece: new modular di- and tridentate stereodirecting ligands

The modular one-pot synthesis of a large family of bi- and tridentate 2,5-dimethyl- and 2,5-diphenyl-substituted phospholanes employs air-stable chiral phospholanium chloride salts and primary amines or NH(4)Cl as starting materials. These were transformed into the C(2)-symmetric dimethyl- and diphenylphospholane ligands, which reacted with [Rh(cod)(2)]BF(4) (cod=1,5-cyclooctadiene) to yield the rhodium complexes [Rh(L)(cod)]BF(4) (L=bisphospholane ligands). The corresponding trisphospholane complexes, 11 and 12, were obtained in high yields (81 and 92%, respectively), and fully characterised by NMR spectroscopy, mass spectrometry and elemental analysis. Whilst in the C(3)-symmetric complex 11, containing the tridentate 2,5-dimethylphospholane, the ligand is bound symmetrically, different coordination behaviour was found for the diphenyl-substituted complex 12, in which the coordination of only two of the three phospholane moieties to the metal centre was observed. A DFT study at the B3PW91 level established minimum energy structures consistent with experimental findings in solution and in the solid state. The non-coordinated phospholane unit present in 12 allowed further modification of the complex through the coordination of Au(I)-X (X=Cl, C(6)F(5) and tris(trifluoromethyl)phenyl ((F)Mes)) fragments to the pendant phosphane. To investigate the potential of the new ligands, the enantioselective hydrogenation of a series of prochiral olefins as benchmark substrates, using isolated Rh complexes as catalysts, was studied. The substrates included methyl esters of three dehydro-α-acetamido acids and two itaconic acid derivatives. In general good to excellent enantioselectivities (of up to >99% ee) were observed. Ligand backbone modification by coordination of bulky Au-X substituents to the free phospholane unit in complex 12 led to an outstanding enhancement of the catalyst performance and there was a clear correlation between the properties of the complex periphery and the enantioselectivity.     

Reduced molybenum-oxide-based core-shell hybrids: "blue" electrons are delocalized on the shell

The present study refers to a variety of reduced metal-oxide core-shell hybrids, which are unique with regard to their electronic structure, their geometry, and their formation. They contain spherical {Mo72Fe30} Keplerate-type shells encapsulating Keggin-type polyoxomolybdates based on very weak interactions. Studies on the encapsulation of molybdosilicate as well as on the earlier reported molybdophosphate, coupled with the use of several physical methods for the characterization led to unprecedented results (see title). Upon standing in air at room temperature, acidified aqueous solutions obtained by dissolving sodium molybdate, iron(II) chloride, acetic acid, and molybdosilicic acid led to the precipitation of monoclinic greenish crystals (1). A rhombohedral variant (2) has also been observed. Upon drying at room temperature, compound 3 with a layer structure was obtained from 1 in a solid-state reaction based on cross-linking of the shells. The compounds 1, 2, and 3 have been characterized by a combination of methods including single-crystal X-ray crystallography, magnetic studies, as well as IR, M?ssbauer, (resonance) Raman, and electronic absorption spectroscopy. In connection with detailed studies of the guest-free two-electron-reduced {Mo72Fe30}-type Keplerate (4) and of the previously reported molybdophosphate-based hybrids (including 31P NMR spectroscopy results), it is unambiguously proved that 1, 2, and 3 contain non-reduced Keggin ion cores and reduced {Mo72Fe30}-type shells. The results are discussed in terms of redox considerations (the shell as well as the core can be reduced) including those related to the reduction of "molybdates" by FeII being of interdisciplinary including catalytic interest (the MoVI/MoV and FeIII/FeII couples have very close redox potentials!), while also referring to the special formation of the hybrids based on chemical Darwinism.     

Evidence for a near-resonant charge transfer mechanism for double-stranded peptide nucleic acid

We present evidence for a near-resonant mechanism of charge transfer in short peptide nucleic acid (PNA) duplexes obtained through electrochemical, STM break junction (STM-BJ), and computational studies. A seven base pair (7-bp) PNA duplex with the sequence (TA)(3)-(XY)-(TA)(3) was studied, in which XY is a complementary nucleobase pair. The experiments showed that the heterogeneous charge transfer rate constant (k(0)) and the single-molecule conductance (σ) correlate with the oxidation potential of the purine base in the XY base pair. The electrochemical measurements showed that the enhancement of k(0) is independent, within experimental error, of which of the two PNA strands contains the purine base of the XY base pair. 7-bp PNA duplexes with one or two GC base pairs had similar measured k(0) and conductance values. While a simple superexchange model, previously used to rationalize charge transfer in single stranded PNA (Paul et al. J. Am. Chem. Soc. 2009, 131, 6498-6507), describes some of the experimental observations, the model does not explain the absence of an enhancement in the experimental k(0) and σ upon increasing the G content in the duplexes from one to two. Moreover, the superexchange model is not consistent with other studies (Paul et al. J. Phys. Chem. B 2010, 114, 14140), that showed a hopping charge transport mechanism is likely important for PNA duplexes longer than seven base pairs. A quantitative computational analysis shows that a near-resonant charge transfer regime, wherein a mix of superexchange and hopping mechanisms are expected to coexist, can rationalize all of the experimental results.     

Enantio- and diastereoselective synthesis of (E)-1,5-syn-diols: application to the synthesis of the C(23)-C(40) fragment of tetrafibricin

A highly stereoselective synthesis of (E)-1,5-syn-diols 6 is described. The kinetically controlled hydroboration of allenyltrifluoroborate 8 with Soderquist borane 2 provides the (Z)-allylic trifluoroborate 9, which undergoes sequential allylboration with two different aldehydes to provide (E)-1,5-syn-diols 6 in 72-98% yields with >95% ee and >20:1 dr. Application of this method to the synthesis of the tetrafibricin C(23)-C(40) fragment 19 is described.     

Simultaneous separation and analysis of water- and fat-soluble vitamins on multi-modal reversed-phase weak anion exchange material by HPLC-UV

Several methods for the separation of vitamins on HPLC columns were already validated in the last 20 years. However, most of the techniques focus on separating either fat- or water-soluble vitamins and only few methods are intended to separate lipophilic and hydrophilic vitamins simultaneously. A mixed-mode reversed-phase weak anion exchange (RP-WAX) stationary phase was developed in our laboratory in order to address such mixture of analytes with different chemical characteristics, which are difficult to separate on standard columns. The high versatility in usage of the RP-WAX chromatographic material allowed a baseline separation of ten vitamins within a single run, seven water-soluble and three fat-soluble, using three different chromatographic modes: some positively charged vitamins are eluted in ion exclusion and ion repulsion modes whereas the negatively charged molecules are eluted in the ion exchange mechanism. The non-charged molecules are eluted in a classical reversed-phase mode, regarding their polarities. The method was validated for the vitamin analysis in tablets, evaluating selectivity, robustness, linearity, accuracy, and precision. The validated method was finally employed for the analysis of the vitamin content of some commercially available supplement tablets.     

Simple monadic theories and indiscernibles

Aiming for applications in monadic second‐order model theory, we study first‐order theories without definable pairing functions. Our main results concern forking‐properties of sequences of indiscernibles. These turn out to be very well‐behaved for the theories under consideration (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)