Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

Optimisation and robustness analysis of a hydrophobic interaction chromatography step

Process development, optimisation and robustness analysis for chromatography separations are often entirely based on experimental work and generic knowledge. The present study proposes a method of gaining process knowledge and assisting in the robustness analysis and optimisation of a hydrophobic interaction chromatography step using a model-based approach. Factorial experimental design is common practice in industry today for robustness analysis. The method presented in this study can be used to find the critical parameter variations and serve as a basis for reducing the experimental work. In addition, the calibrated model obtained with this approach is used to find the optimal operating conditions for the chromatography column. The methodology consists of three consecutive steps. Firstly, screening experiments are performed using a factorial design. Secondly, a kinetic-dispersive model is calibrated using gradient elution and column load experiments. Finally, the model is used to find optimal operating conditions and a robustness analysis is conducted at the optimal point. The process studied in this work is the separation of polyclonal IgG from BSA using hydrophobic interaction chromatography.     

Synthesis of Optically Active endo,endo Bicyclo[2.2.2]octane-2,5-diol, Bicyclo[2.2.2]octane-2,5-dione, and Related Compounds

Optically active C(2)-symmetric (1S,2S,4S,5S)-bicyclo[2.2.2]octane-2,5-diol ((+)-12; 98% ee) and several selectively protected optically active intermediates useful for synthetic transformations were synthesized via a 1,2-carbonyl transposition route starting from the easily available optically active (1R,4S,6S)-6-hydroxybicyclo[2.2.2]octan-2-one ((-)-2). The synthetic route also allowed the preparation of optically active (1S,4S)-bicyclo[2.2.2]octane-2,5-dione ((+)-14; 98% ee).     

Synthesis of 2,3′-biindolyls and indolo[3,2-a]carbazoles

Several highly activated 2,3′-biindolyls were prepared from methyl 5,6-dimethoxyindole-2-carboxylate and oxindoles. The 2,3′-biindolyls were further transformed into a hydroxy indolo[3,2-a]carbazole and a bisindole amide.     

Charge recombination fluorescence in photosystem I reaction centers from Chlamydomonas reinhardtii

The fluorescence kinetics of photosystem I core particles from Chlamydomonas reinhardtii have been measured with picosecond resolution in order to test a previous hypothesis suggesting a charge recombination mechanism for the early electron-transfer steps and the fluorescence kinetics (Müller et al. Biophys. J. 2003, 85, 3899-3922). Performing global target analyses for various kinetic models on the original fluorescence data confirms the "charge recombination" model as the only acceptable one of the models tested while all of the other models can be excluded. The analysis allowed a precise determination of (i) the effective charge separation rate constant from the equilibrated reaction center excited state (438 ns(-1)) confirming our previous assignment based on transient absorption data (Müller et al. Biophys. J. 2003, 85, 3899-3922), (ii) the effective charge recombination rate constant back to the excited state (52 ns(-1)), and (iii) the intrinsic secondary electron-transfer rate constant (80 ns(-1)). The average energy equilibration lifetime core antenna/RC is about 1 ps in the "charge recombination" model, in agreement with previous transient absorption data, vs the 18-20 ps energy transfer lifetime from antenna to RC within "transfer-to-the-trap-limited" models. The apparent charge separation lifetime in the recombination model is about three times faster than in the "transfer-to-the-trap-limited" model. We conclude that the charge separation kinetics is trap-limited in PS I cores devoid of red antenna states such as in C. reinhardtii.     

Measurements and Utilization of Consistent Gibbs Energies of Transfer of Single Ions: Towards a Unified Redox Potential Scale for All Solvents

Utilizing the “ideal” ionic liquid salt bridge to measure Gibbs energies of transfer of silver ions between the solvents water, acetonitrile, propylene carbonate and dimethylformamide results in a consistent data set with a precision of 0.6 kJ mol⁻¹ over 87 measurements in 10 half-cells. This forms the basis for a coherent experimental thermodynamic framework of ion solvation chemistry. In addition, we define the solvent independent - and the values that account for the electronating potential of any redox system similar to the value of a medium that accounts for its protonating potential. This scale is thermodynamically well-defined enabling a straightforward comparison of the redox potentials (reducities) of all media with respect to the aqueous redox potential scale, hence unifying all conventional solvents′ redox potential scales. Thus, using the Gibbs energy of transfer of the silver ion published herein, one can convert and unify all hitherto published redox potentials measured, for example, against ferrocene, to the scale.     

Structure of a surfactant-templated silicate framework in the absence of 3d crystallinity

The structure of a novel molecularly ordered two-dimensional (2D) silicate framework in a surfactant-templated mesophase has been established by using a combination of solid-state nuclear magnetic resonance (NMR) spectroscopy, X-ray diffraction, and quantum chemical and empirical force-field modeling. These materials are unusual in their combination of headgroup-directed 2D crystalline framework ordering, zeolite-like ring structures within the layers, and long-range mesoscopic organization without three-dimensional (3D) atomic periodicity. The absence of registry between the silicate sheets, resulting from the liquidlike disorder of the alkyl surfactant chains, has presented significant challenges to the determination of framework structures in these and similar materials lacking 3D crystalline order. Double-quantum (29)Si NMR correlation experiments establish the interactions and connectivities between distinct intra-sheet silicon sites from which the structure of the molecularly ordered inorganic framework is determined.     

Electrification of a Milstein-type catalyst for alcohol reformation

Novel energy and atom efficiency processes will be keys to develop the sustainable chemical industry of the future. Electrification could play an important role, by allowing to fine-tune energy input and using the ideal redox agent: the electron. Here we demonstrate that a commercially available Milstein ruthenium catalyst (1) can be used to promote the electrochemical oxidation of ethanol to ethyl acetate and acetate, thus demonstrating the four electron oxidation under preparative conditions. Cyclic voltammetry and DFT-calculations are used to devise a possible catalytic cycle based on a thermal chemical step generating the key hydride intermediate. Successful electrification of Milstein-type catalysts opens a pathway to use alcohols as a renewable feedstock for the generation of esters and other key building blocks in organic chemistry, thus contributing to increase energy efficiency in organic redox chemistry.

Electrification of the Milstein catalyst enabled successful molecular electrocatalytic oxidation of ethanol to the four-electron products acetate and ethyl acetate.

In order to achieve the goals of the Sustainable Development Scenario (SDS) of the International Energy Agency, the chemical industry''s emission should decline by around 10% before 2030.^1,2 This could be achieved by increasing energy efficiency and the usage of renewable feedstocks. In this respect, molecular electrocatalytic alcohol oxidation could be powerful tool by potentially providing energy and atom efficiency for organic synthesis and energy applications.^2–7 Besides the use of aminoxyl-derivatives,^8–13 especially the seminal work of Vizza, Bianchini and Grützmacher demonstrated that (transfer)-hydrogenation (TH) catalysts could be activated electrochemically and used in a so-called “organometallic fuel cell”.¹⁴ Other TH systems are however mostly limited to two electron oxidations of secondary or benzylic alcohols (Scheme 1A).^15–21Open in a separate windowScheme 1(A) Advantages/limitation of electrochemical homogeneous alcohol oxidation using well-defined catalysts. (B) Current efforts to electrify acceptor-less alcohol dehydrogenation (AAD) systems due to their large range of application in thermal catalysis.As an exception, Waymouth et al. recently reported an example of the intramolecular coupling of vicinal benzylic alcohols to the corresponding esters.^19,22 In order to extend the range of possible catalysts candidates, the Waymouth group recently also explored the possibility to use an iron-based acceptor-less alcohol dehydrogenation (AAD) catalysts²³ for electrocatalytic alcohol oxidation (Scheme 1B).²⁴ The stability under electrochemical conditions in this case is limited to <2 turnovers, but it opens the door to explore a wide range of AAD reactions under electrochemical conditions. Here, we demonstrate that a commercially available Milstein-type AAD catalyst (1)²⁵ is competent for the electrocatalytic alcohol oxidation of ethanol to ethyl acetate and acetate (Scheme 1B).The cyclic voltammogram (CV) of complex 1 (Fig. 1) shows a quasi-reversible diffusive one electron oxidation wave at 0.2 V (all potentials are referenced vs. Fc⁺/Fc⁰) in 0.2 M NaPF₆ THF/DFB (2 : 1) (DFB = 1,2 difluoro benzene) assigned to the Ru(ii)–Ru(iii) couple (see ESI, section 2.2^†). The addition of 1 to a 10 mM sodium ethoxide (NaOEt) solution in 200 mM ethanol (EtOH) in 0.1 M NaPF₆ (2 : 1 THF/DFB) gives rise to several waves at ca. −0.5, 0.0 and 0.2 V with currents significantly higher than in the absence of catalysts or substrate, indicative of possible catalytic turnover (Fig. 2). Gradual increase of the EtOH concentration from 200 mM to 1 M is accompanied by the disappearance of the first wave at −0.5 V, while a new oxidation wave appears at ca. −0.25 V (Fig. 2, light to dark green traces).Open in a separate windowFig. 1Scan rate dependence of a 1 mM solution of 1 in in 2 : 1 THF/DFB + 0.2 M NaPF6 (from light to dark green: 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5 V s⁻¹, 3 mm GC electrode). Inset: evolution of the peak current as a function of the square root of the scan rate.Open in a separate windowFig. 2CVs of 10 mM NaOEt (grey) and of 5 mM 1 + 5 mM NaOEt with increasing concentrations of EtOH (from light to dark green: 200, 400, 600, 800 and 1000 mM) in 2 : 1 THF/DFB + 0.2 M NaPF₆. Scan rate 0.1 V s⁻¹, electrode: 3 mm diameter GC electrode.Increasing the base loading gradually from 5 to 20 mM yields a stark increase of current at this new wave at ca. −0.25 V (Fig. 3). Using (TBA)PF₆ instead of NaPF₆ (used to avoid Hofmann-elimination²⁶) gave similar results (see ESI, section 2.2–2.5 and section 4^†). In order to assess catalytic turnover under preparative conditions, controlled potential electrolysis (CPE) was performed. CPE experiments were run in pure ethanol (to reduce cell resistance) in the presence of 0.1 M electrolyte of well soluble bases (e.g. NaOEt, LiOH, see ESI section 4^†). CPE in 0.1 M LiOH with 1 mM 1 at E = 0 V vs. Fc^0/+ delivered ca. 15 mM of acetate and 6 mM of ethyl acetate, corresponding to 21 turnovers (per 4 electrons, or 42 turnovers per two electrons) and a faradaic efficiency (FE) of ca. 62% (see ESI section 4.3^†). In the absence of applied potential (OCP, open circuit potential), no ethyl acetate was formed (see ESI, section 4.4^†). Likewise, in the absence of catalyst, the passed charge was significantly lower (7C vs. 40C) with no detected formation of ethyl acetate. The low FE could be due to catalyst degradation, as Ru-nanoparticle formation is observed on the electrode post CPE (confirmed by SEM/Elemental mapping, see ESI section 5^†). Noteworthy, rinse-test CPE and a CPE using a simple Ru-precursor, RuCl₃, did not show any ethyl acetate formation and gave similar results to blank experiments, indicating that Ru-nanoparticles are probably not the active catalyst species and that catalyst instability could be responsible for low FE. Further studies are underway to fully understand catalyst speciation under preparative conditions (see ESI section 4.7^†) the observed catalytic activity of 1 compares well in terms of TON and product selectivity with other molecular homogeneous TH systems, with most systems being limited to the two-electron oxidation of secondary or benzylic alcohols. The Waymouth group reported a NNC ruthenium pincer for the oxidation of isopropanol to acetone with a TON of 4.¹⁸ The same group reported on the usage of phenoxy mediators with an iridium pincer complex, reaching a TON of 8 for the same reaction.²² Bonitatibus and co-workers demonstrated the activity of an iridium-based systems with a TON of 32 for the formation of p-benzaldehyde.¹⁷ Appel and co-workers reported on a nickel (TON = 3.1)¹⁵ and a cobalt triphos systems (TON = 19.9)¹⁶ for benzaldehyde formation from benzyl alcohol. To the best of our knowledge, there is only one acceptor-less alcohol dehydrogenation (AAD) catalyst that has been activated electrochemically so-far,²⁴ generating acetone with a TON <2. Only a handful of molecular systems are known to catalyze the electrochemical four electron alcohol reformation to esters, however at significantly higher potentials (1.15 V vs. Fc⁺/Fc⁰).^2,27,28 Thus, although not designed for electrochemical applications, 1 shows high activity for the challenging 4 electron oxidation of aliphatic substrates.Open in a separate windowFig. 3CV of 5 mM NaOEt (grey), 5 mM of 1 + 1 M EtOH with varying concentrations of base (5, 10, 15, and 20 mM NaOEt, light to dark green) in 2 : 1 THF/DFB + 0.2 M NaPF₆. Scan rate 0.1 V s⁻¹, electrode: 3 mm diameter GC electrode.To achieve the transposition from thermal to electrochemical TH, both Grützmacher et al. and Waymouth took advantage of a fast equilibrium between the alcohol substrate and a metal hydride intermediate that could be readily oxidized. The chemistry of ruthenium pincer AAD systems is well studied (Scheme 2)^25,29–33 and allows for a putative assignment of the observed CV-behavior. In the presence of excess base and alcohol (Fig. 2 and ​and3),3), 1 is expected to yield dearomatized complex 2,²⁵ as well as the alkoxide species 3.^25,32 We might therefore assign the first wave at −0.5 V to the oxidation of dearomatized complex 2 and the wave around 0 V to the oxidation of the alkoxide complex 3. Indeed, independently synthesized samples of 2 and 3 (in the presence of excess ethanol) give rise to oxidation half-waves at −0.45 V and −0.1 V respectively (see ESI, section 3 and 5.2^†). This is also in agreement with the observed behavior upon increasing the alcohol concentration with the expected consumption of dearomatized species 2 and concomitant disappearance of the first oxidation wave at −0.5 V. The equilibrium between 2, 3 and 4 has been reported³² and addition of excess ethanol to 2 is thus not only generating 3, but also is expected to deliver 4 (Scheme 2). The appearance of a new anodic wave at ca. −0.25 V (Fig. 2) is thus attributed to the increasing formation of 4 upon addition of larger amounts of EtOH. Complex 4 is relatively unstable in solution,^25,32,33 and decomposes in the presence of electrolyte (see ESI section 3.1^†). DFT calculations were thus used to predict its oxidation potential (see ESI, section 6^†), which was in reasonable agreement with the observed wave (−0.19 V). The DFT calculations also confirmed the assignment of the other waves related to the dearomatized complex 2 (−0.33 V) and the ethoxide species 3 (−0.1 V). A more detailed mechanistic analysis remains currently hampered by the chemical instability of 4 under the employed reaction conditions, as well as difficulties to isolate 3 in the solid state (limiting kinetic measurements). DFT calculations were thus used to get a better view on possible reaction pathways (Schemes 2, ​,33 and ESI section 6.3^†). The oxidation of 4 at −0.19 V (DFT) yields the radical cation 5, with a calculated pK_a in THF of 8.2. In the presence of NaOEt, 5 should thus deprotonate readily to give radical 6, which has an extremely negative oxidation potential of −2.1 V. At the potential it is generated, 6 should thus directly be oxidized to cationic complex 7. This cationic species 7 has a calculated pK_a of 22.7 in THF, which is in good agreement with experimental data from the Saouma group on a similar system.²⁶ The high pK_a of 7 in THF also validates the need for a strong base (e.g. NaOEt) to reform dearomatized 2. Both Grützmacher and co-workers,¹⁴ as well as Waymouth²⁴ have noted that the accelerating effect during electrocatalysis stems from the oxidation of a metal hydride intermediate that is generated by fast chemical steps. In order to verify this hypothesis and to exclude an electrochemical activation of this hydride formation step, transition state barriers were computed (Scheme 3). Taking the dearomatized complex 2 as a reference point, a first step will form the alkoxide species 3 (TS₀ = 21.2 kcal mol⁻¹). Oxidizing 2 to 8 slows down the formation of the alkoxide species (T_S0^ox = 27.5 kcal mol⁻¹), most-likely due to decreased basicity of the ligand. From the alkoxide species 3 dihydride 4 is formed via a linear, charge-separated transition state TS₁ (15.7 kcal mol⁻¹). The role of such linear transition states was highlighted recently in the case of ruthenium pincer catalysis for alcohol oxidation.^34–37 In principle, it might be envisioned that the oxidation of the metal center could be an additional driving force for this hydride abstraction step. However, after oxidation, the energy span^38,39 rises by about 11 kcal mol⁻¹ (TS₁^ox = 24.7 kcal mol⁻¹). Likewise, a beta-hydride elimination via side-arm opening is not accelerated either by oxidation (TS₂^ox = 37.5 kcal mol⁻¹, see ESI section 6.4^†). It thus seems that the generation of 4 is not accelerated by electron transfer steps and relies on a thermally activated chemical step. Importantly, alkoxide solutions were shown to be excellent hydride donors electrochemically, further corroborating that under the employed basic conditions, generation of 4 from 3 should be fast.⁴⁰ Oxidation of 4 to 5 also doesn''t accelerate thermal intramolecular release of H₂ (TS_3B^ox = 37.5 kcal mol⁻¹), which is significantly higher than neutral thermal H₂-releasing states (TS_3A and TS_3B). The experimentally observed acceleration via electron-transfer is thus proposed to follow a classical ECEC mechanism initiated by the oxidation of 4 to 5 (at roughly −0.19 V (DFT)), followed by deprotonation and re-oxidation as described above, finally delivering 2 at the electrode surface. Importantly, at the electrode surface 2 and 3 should be oxidized at the employed potentials, but based on DFT-calculations, these pathways are thought to be non-productive (Scheme 3) and could explain the low catalyst life-time and degradation under electrochemical conditions.Open in a separate windowScheme 2Reactivity of pyridine-based ruthenium complexes via dearomatization/aromatization, as well as DFT-based.Open in a separate windowScheme 3DFT-calculated energy landscape for the neutral (black dotted lines and bars) and cationic surface (blue dotted lines and bars) of ethanol dehydrogenation starting from 2 or its cationic analogue 8.