Normalizers of irreducible subfactors

We consider normalizers of an infinite index irreducible inclusion N⊆M of II₁ factors. Unlike the finite index setting, an inclusion uNu^∗⊆N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these one-sided normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N^′∩〈M,eN〉 is of the form u^∗eNu for some unitary u∈M with uNu^∗⊆N generalizing the finite index situation considered by Pimsner and Popa. We use this to show that each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of infinite index irreducible subfactors arising from subgroup-group inclusions H⊆G. Here the one-sided normalizers arise from appropriate group elements modulo a unitary from L(H). We are also able to identify the finite trace L(H)-bimodules in ?²(G) as double cosets which are also finite unions of left cosets.     

A Two-Dimensional Computational Droplet Contact Model

The interaction between capillary fluid films and micro-structural rough surfaces is one of the main challenges in studying self-cleaning mechanisms. The surface behavior of the deformable fluid film is governed by the Young-Laplace equation, which is highly non-linear. Therefore, a numerical solution is introduced using the finite element method, based on a continuum mechanical formulation. Surface and line contact at the fluid-structure interface are modeled by enforcing a contact constraint, and a contact angle, respectively. The numerical solution is validated against the analytical solution of a test case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thin film drainage: hydrodynamic and disjoining pressures determined from experimental measurements of the shape of a fluid drop approaching a solid wall

Accurate measurements of the shape of a mercury drop separated from a smooth flat solid surface by a thin aqueous film reported recently by Connor and Horn (Faraday Discuss. 2003, 123, 193-206) have been analyzed to calculate the excess pressure in the film. The analysis is based on calculating the local curvature of the mercury/aqueous interface, and relating it via the Young-Laplace equation to the pressure drop across the interface, which is the difference between the aqueous film pressure and the known internal pressure of the mercury drop. For drop shapes measured under quiescent conditions, the only contribution to film pressure is the disjoining pressure arising from double-layer forces acting between the mercury and mica surfaces. Under dynamic conditions, hydrodynamic pressure is also present, and this is calculated by subtracting the disjoining pressure from the total film pressure. The data, which were measured to investigate the thin film drainage during approach of a fluid drop to a solid wall, show a classical dimpling of the mercury drop when it approaches the mica surface. Four data sets are available, corresponding to different magnitudes and signs of disjoining pressure, obtained by controlling the surface potential of the mercury. The analysis shows that total film pressure does not vary greatly during the evolution of the dimple formed during the thin film drainage process, nor between the different data sets. The hydrodynamic pressure appears to adjust to the different disjoining pressures in such a way that the total film pressure is maintained approximately constant within the dimpled region.     

Matrix-assisted laser desorption/ionization imaging mass spectrometry for direct measurement of clozapine in rat brain tissue

Matrix-assisted laser desorption/ionization hyphenated with quadrupole time-of-flight (QTOF) mass spectrometry (MS) has been used to directly determine the distribution of pharmaceuticals in rat brain tissue slices which might unravel their disposition for new drug development. Clozapine, an antipsychotic drug, and norclozapine were used as model compounds to investigate fundamental parameters such as matrix and solvent effects and irradiance dependence on MALDI intensity but also to address the issues with direct tissue imaging MS technique such as (1) uniform coating by the matrix, (2) linearity of MALDI signals, and (3) redistribution of surface analytes. The tissue sections were coated with various matrices on MALDI plates by airspray deposition prior to MS detection. MALDI signals of analytes were detected by monitoring the dissociation of the individual protonated molecules to their predominant MS/MS product ions. The matrices were chosen for tissue applications based on their ability to form a homogeneous coating of dense crystals and to yield greater sensitivity. Images revealing the spatial localization in tissue sections using MALDI-QTOF following a direct infusion of (3)H-clozapine into rat brain were found to be in good correlation with those using a radioautographic approach. The density of clozapine and its major metabolites from whole brain homogenates was further confirmed using fast high-performance liquid chromatography/tandem mass spectrometry (HPLC-MS/MS) procedures.     

Pressure dependence of pentyl nitrate formation from the OH Radical-initiated reaction of n-pentane in the presence of NO

The formation yields of 2- and 3-pentyl nitrate from the reactions of 2- and 3-pentyl peroxy radicals with NO have been measured at room temperature over the pressure range 51-744 Torr of N2 + O2, using the OH radical-initiated reaction of n-pentane to generate the pentyl peroxy radicals. The influence of 2- and 3-pentyl nitrate formation from the reaction of 2- and 3-pentoxy radicals with NO2 was investigated by conducting experiments with the initial CH3ONO (the OH radical precursor) and NO concentrations being varied by a factor of 5-10. From experiments carried out with low initial CH3ONO and NO concentrations, the measured yields of 2-pentyl nitrate and 3-pentyl nitrate, defined as ([pentyl nitrate] formed)/([n-pentane] reacted), each increase with increasing total pressure, from 1.10 +/- 0.09% and 1.11 +/- 0.10%, respectively, at 51 +/- 1 Torr of O2 to 5.48 +/- 0.51% and 4.07 +/- 0.31%, respectively, at 737 +/- 4 Torr of N2 + O2.     

High-resolution infrared spectroscopy of HCN-Znn (n = 1-4) clusters: structure determination and comparisons with theory

High-resolution infrared laser spectroscopy has been used to obtain rotationally resolved spectra of HCN-Zn(n) (n = 1-4) complexes formed in helium nanodroplets. In the present study the droplets passed through a metal oven, where the zinc vapor pressure was adjusted until one or more atoms were captured by the droplets. A second pickup cell was then used to dope the droplets with a single HCN molecule. Rotationally resolved infrared spectra are obtained for all of these complexes, providing valuable information concerning their structures. Stark spectra are reported and used to determine the corresponding permanent electric dipole moments. Ab initio calculations are also reported for these complexes for comparison with the experimental results.     

Temperature-dependent rate constants for the gas-phase reactions of OH radicals with 1,3,5-trimethylbenzene, triethyl phosphate, and a series of alkylphosphonates

Rate constants for the reactions of OH radicals with dimethyl methylphosphonate [DMMP, (CH3O)2P(O)CH3], dimethyl ethylphosphonate [DMEP, (CH3O)2P(O)C2H5], diethyl methylphosphonate [DEMP, (C2H5O)2P(O)CH3], diethyl ethylphosphonate [DEEP, (C2H5O)2P(O)C2H5], triethyl phosphate [TEP, (C2H5O)3PO] and 1,3,5-trimethylbenzene have been measured over the temperature range 278-348 K at atmospheric pressure of air using a relative rate method. alpha-Pinene (for DEMP, DEEP, TEP and 1,3,5-trimethylbenzene) and di-n-butyl ether (for DMMP and DMEP) were used as the reference compounds, and rate constants for the reaction of OH radicals with di-n-butyl ether were also measured over the same temperature range using alpha-pinene and n-decane as the reference compounds. The Arrhenius expressions obtained for these OH radical reactions (in cm3 molecule(-1) s(-1) units) are 8.00 x 10(-14)e(1470+/-132)/T for DMMP (296-348 K), 9.76 x 10(-14)e(1520+/-14)/T for DMEP (296-348 K), 4.20 x 10(-13)e(1456+/-227)/T for DEMP (296-348 K), 6.46 x 10(-13)e(1339+/-376)/T for DEEP (296-348 K), 4.29 x 10(-13)e(1428+/-219)/T for TEP (296-347 K), and 4.40 x 10(-12)e(738+/-176)/T for 1,3,5-trimethylbenzene (278-347 K), where the indicated errors are two least-squares standard deviations and do not include the uncertainties in the rate constants for the reference compounds. The measured rate constants for di-n-butyl ether are in good agreement with literature data over the temperature range studied (278-348 K).     

Kinetic and product study of the gas-phase reactions of OH radicals, NO(3) radicals, and O(3) with (C(2)H(5)O)(2)P(S)CH(3) and (C(2)H(5)O)(3)PS

Rate constants for the reactions of OH radicals and NO3 radicals with O,O-diethyl methylphosphonothioate [(C(2)H(5)O)(2)P(S)CH(3); DEMPT] and O,O,O-triethyl phosphorothioate [(C(2)H(5)O)(3)PS; TEPT] have been measured using relative rate methods at atmospheric pressure of air over the temperature range 296-348 K for the OH radical reactions and at 296 +/- 2 K for the NO(3) radical reactions. At 296 +/- 2 K, the rate constants obtained for the OH radical reactions (in units of 10(-11) cm(3) molecule(-1) s(-1)) were 20.4 +/- 0.8 and 7.92 +/- 0.27 for DEMPT and TEPT, respectively, and those for the NO(3) radical reactions (in units of 10(-15) cm(3) molecule(-1) s(-1)) were 2.01 +/- 0.20 and 1.03 +/- 0.10, respectively. Upper limits to the rate constants for the reactions of O(3) with DEMPT and TEPT of <6 x 10(-20) cm(3) molecule(-1) s(-1) were determined in each case. Rate constants for the OH radical reactions, measured relative to k(OH + alpha-pinene) = 1.21 x 10(-11) e(436/T) cm(3) molecule(-1) s(-1), resulted in the Arrhenius expressions k(OH + DEMPT) = 1.08 x 10(-11) e(871+/-25)/T cm(3) molecule(-1) s(-1) and k(OH + TEPT) = 8.21 x 10(-13) e(1353+/-49)/T cm(3) molecule(-1) s(-1) over the temperature range 296-348 K, where the indicated errors are two least-squares standard deviations and do not include the uncertainties in the reference rate constant. Diethyl methylphosphonate was identified and quantified from the OH radical and NO(3) radical reactions with DEMPT, with formation yields of 21 +/- 4%, independent of temperature, from the OH radical reaction and 62 +/- 11% from the NO(3) radical reaction at 296 +/- 2 K. Similarly, triethyl phosphate was identified and quantified from the OH radical and NO(3) radical reactions with TEPT, with formation yields of 56 +/- 9%, independent of temperature, from the OH radical reaction and 78 +/- 15% from the NO(3) radical reaction at 296 +/- 2 K.     

Structures and bonding nature of small monoligated copper clusters (HCN-Cun, n = 1-3) through high-resolution infrared spectroscopy and theory

The structures, C-H stretching frequencies, and dipole moments of HCN-Cun (n = 1-3) clusters are determined through high-resolution infrared spectroscopy. The complexes are formed and probed within superfluid helium droplets, whereby the helium droplet beam is passed over a resistively heated crucible containing copper shot and then through a gas HCN pickup cell. All complexes are found to be bound to the nitrogen end of the HCN molecule and on the "atop site" of the copper cluster. Through the experimental C-H vibrational shifts of HCN-Cun and ab initio calculations, it was found that the HCN-metal interaction changes from a strong van der Waals bond in n = 1 to a partially covalent bond in HCN-Cu3. Comparisons with existing infrared data on copper surfaces show that the HCN-Cun bond must begin to weaken at very large copper cluster sizes, eventually returning to a van der Waals bond in the bulk copper surface case.     

Photophysical properties of a rhodium tetraphenylporphyrin-tin corrole dyad. The first example of a through metal-metal bond energy transfer

The luminescence spectroscopy study and the determination of the photophysical parameters for the M-M'-bonded rhodium meso-tetraphenylporphyrin-tin(2,3,7,13,17,18-hexamethyl-8,12-diethylcorrole) complex, (TPP)Rh-Sn(Me6Et2Cor) 1, was investigated. The emission bands as well as the lifetimes (tau(e)) and the quantum yields (Phi(e); at 77 K using 2MeTHF as solvent) were compared with those of (TPP)RhI 2 (TPP = tetraphenylporphyrin) and (Me6Et2Cor)SnCl 3 (Me6Et2Cor = 2,3,7,13,17,18-hexamethyl-8,12-diethylcorrole) which are the two chemical precursors of 1. The energy diagram has been established from the absorption, fluorescence and phosphorescence spectra. The Rh(TPP) and Sn(Me6Et2Cor) chromophores are the energy donor (D) and acceptor (A), respectively. The total absence of fluorescence in 1 (while fluorescence is observed in the tin derivative 3) indicates efficient excited state deactivation, presumably due to heavy atom effect and intramolecular energy transfer (ET). The large decreases in tau(P) and Phi(P) of the Rh(TPP) chromophore going from 2 to 1 indicate a significant intramolecular ET in the triplet states of 1 with an estimated rate ranging between 10(6) and 10(8) s(-1). Based on the comparison of transfer rates with other related dyads that exhibit similar D-A separations and no M-M' bond, and for which slower through space ET processes (10(2)-10(3) s(-1)) operate, a through M-M' bond ET has been unambiguously assigned to 1.