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.     

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.     

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.     

Subcomponent self-assembly of circular helical Dy6(L)6 and bipyramid Dy12(L)8 architectures directed via second-order template effects

In situ metal-templated (hydrazone) condensation also called subcomponent self-assembly of 4,6-dihydrazino-pyrimidine, o-vanillin and dysprosium ions resulted in the formation of discrete hexa- or dodecanuclear metallosupramolecular Dy₆(L)₆ or Dy₁₂(L)₈ aggregates resulting from second-order template effects of the base and the lanthanide counterions used in these processes. XRD analysis revealed unique circular helical or tetragonal bipyramid architectures in which the bis(hydrazone) ligand L adopts different conformations and shows remarkable differences in its mode of metal coordination. While a molecule of trimethylamine acts as a secondary template that fills the void of the Dy₆(L)₆ assembly, sodium ions take on this role for the formation of heterobimetallic Dy₁₂(L)₈ by occupying vacant coordination sites, thus demonstrating that these processes can be steered in different directions upon subtle changes of reaction conditions. Furthermore, Dy₆(L)₆ shows an interesting spin-relaxation energy barrier of 435 K, which is amongst the largest values within multinuclear lanthanide single-molecular magnets.

Subcomponent self-assembly gave access to Dy₁₂(L)₈ and Dy₆(L)₆ architectures via second-order template effects. The Dy₆(L)₆ assembly behaves as a single-molecule magnet exhibiting a high anisotropy barrier and butterfly-shaped magnetic hysteresis.     

Selective oxidation of silanes into silanols with water using [MnBr(CO)5] as a precatalyst

The development of earth-abundant catalysts for the selective conversion of silanes to silanols with water as an oxidant generating valuable hydrogen as the only by-product continues to be a challenge. Here, we demonstrate that [MnBr(CO)₅] is a highly active precatalyst for this reaction, operating under neutral conditions and avoiding the undesired formation of siloxanes. As a result, a broad substrate scope, including primary and secondary silanes, could be converted to the desired products. The turnover performances of the catalyst were also examined, yielding a maximum TOF of 4088 h⁻¹. New light was shed on the debated mechanism of the interaction between [MnBr(CO)₅] and Si–H bonds based on the reaction kinetics (including KIEs of PhMe₂SiD and D₂O) and spectroscopic techniques (FT-IR, GC-TCD, ¹H-, ²⁹Si-, and ¹³C-NMR). The initial activation of [MnBr(CO)₅] was found to result from the formation of a manganese(i) hydride species and R₃SiBr, and the experimental data are most consistent with a catalytic cycle comprising a cationic tricarbonyl Mn(i) unit as the active framework.

This study presents the use of MnBr(CO)₅ for the selective conversion of silanes to silanols with water as an oxidant generating valuable hydrogen as the only by-product.     

Correlating conductivity and Seebeck coefficient to doping within crystalline and amorphous domains in poly(3-(methoxyethoxyethoxy)thiophene)

Molecular doping of conjugated polymers (CPs) plays a vital role in optimizing organic electronic and energy applications. For the case of organic thermoelectrics, it is commonly believed that doping CPs with a strong dopant could result in higher conductivity (σ) and thus better power factor (PF). Herein, by investigating thermoelectric performance of a polar side-chain bearing CP, poly(3-(methoxyethoxyethoxy)thiophene) (P3MEET), vapor doped with fluorinated-derivative of tetracyanoquinodimethane FnTCNQ (n = 1, 2, 4), we show that using strong dopants can in fact have detrimental effects on the thermoelectric performance of CPs. Despite possessing higher electron affinity, doping P3MEET with F4TCNQ only results in a σ (27.0 S/cm) comparable to samples doped with other two weaker dopants F2TCNQ and F1TCNQ (26.4 and 20.1 S/cm). Interestingly, F4TCNQ-doped samples display a marked reduction in the Seebeck coefficient (α) compared to F1TCNQ- and F2TCNQ-doped samples from 42 to 13 μV/K, leading to an undesirable suppression of the PF. Structural characterizations coupled with Kang-Snyder modeling of the α–σ relation show that the reduction of α in F4TCNQ-doped P3MEET samples originates from the generation of low mobility carrier within P3MEET's amorphous domain. Our results demonstrate that factors such as dopant distribution and doping efficiency within the crystalline and amorphous domains of CPs should play a crucial role in advancing rational design for organic thermoelectrics.     

Oxydationslösungen von Humussäuren und verwandten Stoffen

Ohne Zusammenfassung     

Sterically Allowed H-type Supramolecular Polymerizations

The functionalization of π-conjugated scaffolds with sterically demanding substituents is a widely used tactic to suppress cofacial (H-type) stacking interactions, which may even inhibit self-assembly. Contrary to expectations, we demonstrate herein that increasing steric effects can result in an enhanced thermodynamic stability of H-type supramolecular polymers. In our approach, we have investigated two boron dipyrromethene (BODIPY) dyes with bulky phenyl ( 2 ) and mesityl ( 3 ) meso-substituents and compared their self-assembly in nonpolar media with that of a parent meso-methyl BODIPY 1 lacking bulky groups. While the enhanced steric demand induces pathway complexity, the superior thermodynamic stability of the H-type pathways can be rationalized in terms of additional enthalpic gain arising from intermolecular C−H⋅⋅⋅F−B interactions of the orthogonally arranged aromatic substituents, which overrule their inherent steric demand. Our findings underline the importance of balancing competing non-covalent interactions in self-assembly.     

Optimization of preparative chromatographic separation of multiple rare earth elements

This work presents a method to optimize multi-product chromatographic systems with multiple objective functions. The system studied is a neodymium, samarium, europium, gadolinium mixture separated in an ion exchange chromatography step. A homogeneous Langmuir Mobile Phase Modified model is calibrated to fit the experiments, and then used to perform the optimization task. For the optimization a multi-objective Differential Evolution algorithm was used, with weighting based on relative value of the components to find optimal operation points along the Pareto front. The objectives of the Pareto front are weighted productivity and weighted yield with purity as an equality constraint. A prioritizing scheme based on relative values is applied for determining the pooling order. A simple rule of thumb for pooling strategy selection is presented. The multi-objective optimization gives a Pareto front which shows the rule of thumb, as a gap in one of the objective functions.