Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-order implicit schemes

Journal of Thermal Analysis and Calorimetry - Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve...     

Self-bonding in an amorphous polymer below the glass transition: A T-peel test investigation

Films of amorphous polystyrene (PS) with a weight-average molecular weight (M_w) of 225 × 10³ g/mol were bonded in a T-peel test geometry, and the fracture energy (G) of a PS/PS interface was measured at the ambient temperature as a function of the healing time (t_h) and healing temperature (T_h). G was found to develop with (t_h)^1/2 at T_h = T_g-bulk − 33 °C (where T_g-bulk is the glass-transition temperature of the bulk sample), and log G was found to develop with 1/T_h at T_g-bulk − 43 °C ≤ T_h ≤ T_g-bulk − 23 °C. The smallest measured value of G = 1.4 J/m² was at least one order of magnitude larger than the work of adhesion required to reversibly separate the PS surfaces. These three observations indicated that the development of G at the PS/PS interface in the temperature range investigated (<T_g-bulk) was controlled by the diffusion of chain segments feasible above the glass-transition temperature of the interfacial layer, in agreement with our previous findings for fracture stress development at several polymer/polymer interfaces well below T_g-bulk. Close values of G = 8–9 J/m² were measured for the symmetric interfaces of polydisperse PS [M_w = 225 × 10³, weight-average molecular weight/number-average molecular weight (M_w/M_n) = 3] and monodisperse PS (M_w = 200 × 10³, M_w/M_n = 1.04) after healing at T_h = T_g-bulk − 33 °C for 24 h. This implies that the self-bonding of high-molecular-weight PS at such relatively low temperatures is not governed by polydispersity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1861–1867, 2004     

An expedient synthesis of an isofervenulin analogue

An efficient approach has been developed for the synthesis of an isofervenulin analogue 1 employing a one‐pot condensation‐substitution reaction of a chlorocarboethoxytriazine (electrophile) with a urea (nucleophile). The resulting cyclization reaction resulted in the synthesis of a pyrimido‐heterocycle in good yield in either acidic or basic media. The former was assisted by utilizing trimethylsilyl chloride.     

Zur Thermodynamischen Begründung der Kovats'schen Retentionsindizes

Chromatographia - Ausgehend von den thermodynamischen Grundlagen wird die Siedepunktsabhängigkeit der Retentionszeiten diskutiert. Über eine Formel vonKlages, nach der sich das Quadrat...     

High facial diastereoselectivity in intra- and intermolecular reactions of chiral benzylic cations

Chiral carbenium ions can be attacked by arene nucleophiles with high facial diastereoselectivity (dr >/= 94/6). Benzylic cations, such as 2, were generated under acidic conditions and reacted with arenes in intra- and intermolecular Friedel-Crafts alkylation reaction. The depicted reaction 1 --> 3 represents one example for the unprecedented, highly diastereoselective intermolecular Friedel-Crafts alkylation reactions which were observed in this study.     

Chemical behavior of the biradicaloid (HO...ONO) singlet states of peroxynitrous acid. The oxidation of hydrocarbons, sulfides, and selenides

Various high levels of theory have been applied to the characterization of two higher lying biradicaloid metastable singlet states of peroxynitrous acid. A singlet minimum (cis-2) was located that had an elongated O-O distance (2.17 A) and was only 12.2 kcal/mol [UB3LYP/6-311+G(3df,2p)+ZPVE] higher in energy than its ground-state precursor. A trans-metastable singlet (trans-2) was 10.9 kcal/mol higher in energy than ground-state HO-ONO. CASSCF(12,10)/6-311+G(d,p) calculations predict the optimized geometries of these cis- and trans-metastable singlets to be close to those obtained with DFT. Optimization of cis- and trans-2 within the COSMO solvent model suggests that both exist as energy minima in polar media. Both cis- and trans-2 exist as hydrogen bonded complexes with several water molecules. These collective data suggest that solvated forms of cis-2.3H(2)O and trans-2.3H(2)O represent the elusive higher lying biradicaloid minima that were recently (J. Am. Chem. Soc. 2003, 125, 16204) advocated as the metastable forms of peroxynitrous acid (HOONO). The involvement of metastable trans-2 in the gas phase oxidation of methane and isobutane is firmly established to take place on the unrestricted [UB3LYP/6-311+G(d,p)] potential energy surface (PES) with classical activations barriers for the hydrogen abstraction step that are 15.7 and 5.9 kcal/mol lower than the corresponding activation energies for producing products methanol and tert-butyl alcohol formed on the restricted PES. The oxidation of dimethyl sulfide and dimethyl selenide, two-electron oxidations, proceeds by an S(N)2-like attack of the heteroatom lone pair on the O-O bond of ground-state peroxynitrous acid. No involvement of metastable forms of HO-ONO was discernible.     

Results and estimates on pseudopowers

Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.