The free boundary problem of a semiconductor in thermal equilibrium

The quasi-hydrodynamic model for semiconductor devices in thermal equilibrium admits in general solutions for which the electron or hole density vanish. These sets are called vacuum sets. In this paper estimates on the vacuum sets and a first step in the regularity of the free boundary of these sets are presented. Numerical examples, including error estimates for linear finite elements, for the devices diode, bipolar transistor and thyristor indicate that the free boundary is more regular than theoretically predicted.     

MultiMCS: a fast algorithm for the maximum common substructure problem on multiple molecules

Several efficient correspondence graph-based algorithms for determining the maximum common substructure (MCS) of a pair of molecules have been published in the literature. The extension of the problem to three or more molecules is however nontrivial; heuristics used to increase the efficiency in the two-molecule case are either inapplicable to the many-molecule case or do not provide significant speedups. Our specific algorithmic contribution is two-fold. First, we show how the correspondence graph approach for the two-molecule case can be generalized to obtain an algorithm that is guaranteed to find the optimum connected MCS of multiple molecules, and that runs fast on most families of molecules using a new divide-and-conquer strategy that has hitherto not been reported in this context. Second, we provide a characterization of those compound families for which the algorithm might run slowly, along with a heuristic for speeding up computations on these families. We also extend the above algorithm to a heuristic algorithm to find the disconnected MCS of multiple molecules and to an algorithm for clustering molecules into groups, with each group sharing a substantial MCS. Our methods are flexible in that they provide exquisite control on various matching criteria used to define a common substructure.     

Phase Biaxility in Smectic‐A Side‐Chain Liquid Crystalline Elastomers

²H NMR investigations on the biaxial phase behavior of smectic‐A liquid crystalline side‐chain elastomers are presented. Biaxiality parameters were determined by measuring the quadrupolar splitting of two spin probes, namely benzene‐d₆ and hexamethylbenzene‐d₁₈, at various angles between the principal director and the external magnetic field: while for a uniaxial sample the angular dependence can be described by the second Legendre polynomial, an additional asymmetric term needs to be included to fit the data of the two investigated biaxial systems. Two elastomers synthesized from mesogens that differ in the molecular geometry in order to study the molecular origin of biaxiality were compared. Biaxiality is observed for both elastomers when approaching the glass transition, suggesting that the network dynamics dominate the formation of the biaxial phase.

     

Prediction of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl) amide ionic liquids

The vapor pressures and vaporization enthalpies of a series of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl) amide ionic liquids have been predicted with two different approaches using the COSMO-RS method and quantum chemical gas phase calculations. While the calculated enthalpies are in good agreement with the experimental data, COSMO-RS seems to underestimate the vapor pressures by roughly 0.5-4 log units dependent on the IL and approach used.     

Coupling of a High-Resolution Ambient Pressure Drift Tube Ion Mobility Spectrometer to a Commercial Time-of-flight Mass Spectrometer

Ion mobility spectrometry provides information about molecular structures of ions. Hence, high resolving power allows separation of isomers which is of major interest in several applications. In this work, we couple our high-resolution ion mobility spectrometer (IMS) with a resolving power of R_p?=?100 to a time-of-flight mass spectrometer (TOF-MS). Besides, the benefit of an increased resolving power such an IMS-MS also helps analyzing and understanding the ionization processes in IMS. Usually, the coupling between IMS and TOF-MS is realized by synchronizing data acquisition of the IMS and MS resulting in two-dimensional data containing ion mobility and mass spectra. However, due to peak widths of less than 100 μs in our high-resolution IMS, this technique is not practicable due to significant peak broadening during the ion transfer into the MS and an insufficient data acquisition rate of the MS. Thus, a novel but simple interface between the IMS and MS has been designed which minimizes ion losses, allows recording of ion mobility at full IMS resolving power, and enables a shuttered transmission of ions into the MS. The interface is realized by replacing the Faraday plate used in IMS by a Faraday grid that is shielded by two additional aperture grids. For demonstration, positive product ions of benzene, toluene, and m-xylene in air are investigated. The IMS is equipped with a radioactive ³H source. Besides the well-known product ions M⁺ and M·NO⁺, a dimer ion is also observed for benzene and toluene, consisting of two molecules and three further hydrogen atoms.

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TheW-boson width

The analytic formulae for the partial decay widthW ⁺→ \(f_1 \bar f_2 \) are presented including the 1-loop electroweak and QCD corrections for arbitrary masses of the fermions. Numerical results are discussed for the physically interesting cases \(W^ + \to t\bar b\) and for the decay into a heavy leptonl ⁺ and a neutrino of a fourth fermion generation. Also the results for the totalW width and the partial width into light fermion pairs are listed.     

Surprisingly Different Reaction Behavior of Alkali and Alkaline Earth Metal Bis(trimethylsilyl)amides toward Bulky N‐(2‐Pyridylethyl)‐N′‐(2,6‐diisopropylphenyl)pivalamidine

N‐(2,6‐Diisopropylphenyl)‐N′‐(2‐pyridylethyl)pivalamidine (Dipp‐N=C(tBu)‐N(H)‐C₂H₄‐Py) ( 1 ), reacts with metalation reagents of lithium, magnesium, calcium, and strontium to give the corresponding pivalamidinates [(tmeda)Li{Dipp‐N=C(tBu)‐N‐C₂H₄‐Py}] ( 6 ), [Mg{Dipp‐N=C(tBu)‐N‐C₂H₄‐Py}₂] ( 3 ), and heteroleptic [{(Me₃Si)₂N}Ae{Dipp‐N=C(tBu)‐N‐C₂H₄‐Py}], with Ae being Ca ( 2 a ) and Sr ( 2 b ). In contrast to this straightforward deprotonation of the amidine units, the reaction of 1 with the bis(trimethylsilyl)amides of sodium or potassium unexpectedly leads to a β‐metalation and an immediate deamidation reaction yielding [(thf)₂Na{Dipp‐N=C(tBu)‐N(H)}] ( 4 a ) or [(thf)₂K{Dipp‐N=C(tBu)‐N(H)}] ( 4 b ), respectively, as well as 2‐vinylpyridine in both cases. The lithium derivative shows a similar reaction behavior to the alkaline earth metal congeners, underlining the diagonal relationship in the periodic table. Protonation of 4 a or the metathesis reaction of 4 b with CaI₂ in tetrahydrofuran yields N‐(2,6‐diisopropylphenyl)pivalamidine (Dipp‐N=C(tBu)‐NH₂) ( 5 ), or [(thf)₄Ca{Dipp‐N=C(tBu)‐N(H)}₂] ( 7 ), respectively. The reaction of AN(SiMe₃)₂ (A=Na, K) with less bulky formamidine Dipp‐N=C(H)‐N(H)‐C₂H₄‐Py ( 8 ) leads to deprotonation of the amidine functionality, and [(thf)Na{Dipp‐N=C(H)‐N‐C₂H₄‐Py}]₂ ( 9 a ) or [(thf)K{Dipp‐N=C(H)‐N‐C₂H₄‐Py}]₂ ( 9 b ), respectively, are isolated as dinuclear complexes. From these experiments it is obvious, that β‐metalation/deamidation of N‐(2‐pyridylethyl)amidines requires bases with soft metal ions and also steric pressure. The isomeric forms of all compounds are verified by single‐crystal X‐ray structure analysis and are maintained in solution.     

Zinc Silicates: Very Efficient Heterogeneous Catalysts for the Addition of Primary Alcohols to Alkynes and Allenes

There is an astonishing parallel between the mechanism generally accepted for the addition of water to CO₂ catalyzed by the enzyme carbonic anhydrase and the mechanism calculated for the addition of methanol to allene catalyzed by the naturally occurring zinc silicate hemimorphite. The latter reaction was investigated in detail following the observation that hemimorphite as well as an amorphous zinc silicate prepared in situ are excellent heterogeneous catalysts for the addition of primary alcohols to alkynes and allenes [Eq. (1)].     

Size Complementarity of Macrocyclic Cavities and Stoppers in Amide-Rotaxanes

New [2]rotaxanes were prepared by the threading and the slipping procedure, the latter having the advantage of not needing templating interactions. As a consequence, the first [2]rotaxane consisting of a tetraamide macrocycle and a pure hydrocarbon thread was synthesized (see 12a in Scheme 2). Sterically matching wheels and axles being the basic requirement of a successful slipping approach to rotaxanes, mono- and bishomologous wheels 5b , c with larger diameters than the parent 5a were synthesized and mechanically connected to amide axles 10a – c which were stoppered with blocking groups of different spatial demand (Scheme 1). The deslipping kinetics of the resulting rotaxanes 8a – c and 9a , b were measured and compared; it emerges that even slight increases in the wheel size require larger stoppers to stabilize the mechanical bond. Moreover, when the deslipping rate of 8a (amide wheel and amide axle) was determined in either DMF or THF, a strong dependence on the solvent polarity, which is caused by a differing extent of intramolecular H-bonds between the wheel and the axle, was observed. As expected, no such dependence was detected for rotaxane 12a (amide wheel and hydrocarbon axle) whose components cannot interact via H-bonds. The comparison of the sterically matching pairs of macrocycles and blocking groups, found by a systematic fitting based on the results of slipping and deslipping experiments, with other rotaxane types bearing similar stoppers allows conclusions concerning the relative cavity size of wheels of various structure.