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     

New methodologies in trace analysis of volatile organic compounds

Two methods for sampling and concentration of volatile organic compounds are reported. In the first method, traps coated with a very thick film (ca. 100 μm) of cross-linked silicone stationary phase are employed. Such thick films can be prepared with a modified dynamic coating procedure, which is briefly described. The low phase ratio traps can be utilized for enrichment of volatiles from gaseous as well as aqueous matrices. The second technique is based on chromatographic evaporation of a solvent in a capillary tube, where the process is sustained by a repeated sample injection and a cyclic flow reversal. In this way, large solvent volumes can be handled by a small volume system. Under optimal conditions, when using a solvent barrier, quantitative recovery is possible even for compounds of comparatively high volatility. Another important application of the technique is extraction of trace components from gases such as headspace samples, polluted air, etc.     

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.     

A technique for coating capillary columns with a very thick film of cross-linked stationary phase

A method for preparation of capillary columns and traps with a very thick film (up to 100 μm) of stationary phase is described. The principle of this method is based on an immediate fixation of a film of prepolymer, formed during dynamic coating. Thus, the development of film irregularities, such as are caused by Rayleigh instability is avoided. Fixation of the film is conveniently accomplished by heat-accelerated crosslinking as was demonstrated in this work, where a commercially available silicone prepolymer (Sylgard 184, Dow Corning) was employed. The low phase ratio columns which thus can be prepared are interesting both in chromatography with dense mobile phases and as enrichment devices. Examples of the latter application are shown, where trace organic components from air and water were concentrated.     

A mechanism from quantum chemical studies for methane formation in methanogenesis

The mechanism for methane formation in methyl-coenzyme M reductase (MCR) has been investigated using the B3LYP hybrid density functional method and chemical models consisting of 107 atoms. The experimental X-ray crystal structure of the enzyme in the inactive MCR(ox1)(-)(silent) state was used to set up the initial model structure. The calculations suggest a mechanism not previously proposed, in which the most remarkable feature is the formation of an essentially free methyl radical at the transition state. The reaction cycle suggested starts from a Michaelis complex with CoB and methyl-CoM coenzymes bound and with a squareplanar coordination of the Ni(I) center in the tetrapyrrole F(430) prosthetic group. In the rate-limiting step the methyl radical is released from methyl-CoM, induced by the attack of Ni(I) on the methyl-CoM thioether sulfur. In this step, the metal center is oxidized from Ni(I) to Ni(II). The resulting methyl radical is rapidly quenched by hydrogen-atom transfer from the CoB thiol group, yielding the methane molecule and the CoB radical. The estimated activation energy is around 20 kcal/mol, which includes a significant contribution from entropy due to the formation of the free methyl. The mechanism implies an inversion of configuration at the reactive carbon. The size of the inversion barrier is used to explain the fact that CF(3)-S-CoM is an inactive substrate. Heterodisulfide CoB-S-S-CoM formation is proposed in the final step in which nickel is reduced back to Ni(I). The suggested mechanism agrees well with experimental observations.     

A density functional study on a biomimetic non-heme iron catalyst: insights into alkane hydroxylation by a formally HO-FeV=O oxidant

The reactivity of [HO-(tpa)Fe(V)=O] (TPA=tris(2-pyridylmethyl)amine), derived from O-O bond heterolysis of its [H(2)O-(tpa)Fe(III)-OOH] precursor, was explored by means of hybrid density functional theory. The mechanism for alkane hydroxylation by the high-valent iron-oxo species invoked as an intermediate in Fe(tpa)/H(2)O(2) catalysis was investigated. Hydroxylation of methane and propane by HO-Fe(V)=O was studied by following the rebound mechanism associated with the heme center of cytochrome P450, and it is demonstrated that this species is capable of stereospecific alkane hydroxylation. The mechanism proposed for alkane hydroxylation by HO-Fe(V)=O accounts for the experimentally observed incorporation of solvent water into the products. An investigation of the possible hydroxylation of acetonitrile (i.e., the solvent used in the experiments) shows that the activation energy for hydrogen-atom abstraction by HO-Fe(V)=O is rather high and, in fact, rather similar to that of methane, despite the similarity of the H-CH(2)CN bond strength to that of the secondary C-H bond in propane. This result indicates that the kinetics of hydrogen-atom abstraction are strongly affected by the cyano group and rationalizes the lack of experimental evidence for solvent hydroxylation in competition with that of substrates such as cyclohexane.     

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.     

Illustration of a simple and versatile scheme for reversing enantiomeric elution order and facilitating enantiomeric impurity determination in capillary electrophoresis

Determination of enantiomeric purity is most often done under overload conditions, which leads to deformed peaks. In general, the best resolutions are obtained when the small peak appears before the large peak in the electropherogram. To be able to determine the R(+)-impurity in the S(-)-form as well as the S(-)-impurity in the R(+)-form the elution orders have to be reversed. The present paper describes reversal of enantiomeric elution order for the basic analyte propranolol and the acidic analyte ibuprofen. For propranolol, a charged heptakis-(6-sulfo)-beta-cyclodextrin (CD) is used in the background electrolyte. For ibuprofen, a mix of the charged heptakis-(6-sulfo)-beta-CD and the uncharged heptakis-(2,3,6-tri-O-methyl)-beta-CD is used in the background electrolyte. The use of a coated capillary and reversal of the polarity shift the elution order, buffer composition is unchanged in both cases. The enantiomers of propranolol and ibuprofen are well separated on both the coated and uncoated capillaries. Detection limits of enantiomer impurities are investigated using spiked samples of both propranolol and ibuprofen.     

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).