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.     

Prediction of Propagation Rate Coefficients in Free Radical Solution Polymerization Based on Accurate Quantum Chemical Methods: Vinylic and Related Monomers,Including Acrylates and Acrylic Acid

The simulation of polymerization processes is of enormous industrial importance. A quantum chemical method based on density functional theory is developed and validated that provides almost chemical accuracy for radical polymerization propagation of industrially relevant monomers in aqueous solution. The necessary corrections are computed using the CC level of theory. Solvent effects are accounted for by the solvation model COSMO‐RS. The method is capable of reproducing and rationalizing, for example, monomer concentration effects on the propagation rate for NVP. A comparison is performed with recent PLP experimental data. The method does not rely on error compensation effects or empiric corrections and is suitable for industrially relevant systems.

     

The relaxation-time limit in the quantum hydrodynamic equations for semiconductors

The relaxation-time limit from the quantum hydrodynamic model to the quantum drift-diffusion equations in R³ is shown for solutions which are small perturbations of the steady state. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density including the quantum Bohm potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. The relaxation-time limit is performed both in the stationary and the transient model. The main assumptions are that the steady-state velocity is irrotational, that the variations of the doping profile and the velocity at infinity are sufficiently small and, in the transient case, that the initial data are sufficiently close to the steady state. As a by-product, the existence of global-in-time solutions to the quantum drift-diffusion model in R³ close to the steady-state is obtained.     

A Degenerate Fourth-Order Parabolic Equation Modeling Bose-Einstein Condensation Part II: Finite-Time Blow-Up

A degenerate fourth-order parabolic equation modeling condensation phenomena related to Bose-Einstein particles is analyzed. The model can be motivated from the spatially homogeneous and isotropic Boltzmann-Nordheim equation by a formal Taylor expansion of the collision integral. It maintains some of the main features of the kinetic model, namely mass and energy conservation and condensation at zero energy. The existence of local-in-time weak solutions satisfying a certain entropy inequality is proven. The main result asserts that if a weighted L ¹ norm of the initial data is sufficiently large and the initial data satisfies some integrability conditions, the solution blows up with respect to the L ^∞ norm in finite time. Furthermore, the set of all such blow-up enforcing initial functions is shown to be dense in the set of all admissible initial data. The proofs are based on approximation arguments and interpolation inequalities in weighted Sobolev spaces. By exploiting the entropy inequality, a nonlinear integral inequality is proved which implies the finite-time blow-up property.     

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.