Determination of fluid-phase behavior using transition-matrix Monte Carlo: binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.     

Hidden variables and locality

Bell's problem of the possibility of a local hidden variable theory of quantum phenomena is considered in the context of the general problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space, and Bell's result is presented as a generalization of Maczynski's theorem for maximal magnitudes. The proof of this generalization is shown to depend on the impossibility of recovering the quantum statistics for sequential probabilities in a classical representation without introducing a randomization process for the hidden variables. Hidden variable theories that exclude such a randomization process are termed strict, and it is shown that the class of local hidden variable theories is included in the class of strict theories. A counterargument by Freedman and Wigner is evaluated with reference to Clauser's extension of a hidden variable model proposed by Bell.     

Actions of Commutative Hopf Algebras

We show that actions of finite-dimensional semisimple commutativeHopf algebras H on H-module algebras A are essentially group-gradings.Moreover we show that the centralizer of H in the smash productA # H equals A^H H. Using these we invoke results about groupgraded algebras and results about centralizers of separablesubalgebras to give connections between the ideal structureof A, A^H and A # H. Examples of the above occur naturally when one considers: (1) finite abelian groups G of automorphisms of an algebra Awith | G |^–1 A; (2) G-graded algebras, for finite groups G; (3) finite-dimensional restricted Lie algebras L, with semisimplerestricted enveloping algebra u(L), acting as derivations onan algebra A.     

Measurement of the elastic modulus of single bacterial cellulose fibers using atomic force microscopy

The ability of the atomic force microscope to measure forces with subnanonewton sensitivity at nanometer-scale lateral resolutions has led to its use in the mechanical characterization of nanomaterials. Recent studies have shown that the atomic force microscope can be used to measure the elastic moduli of suspended fibers by performing a nanoscale three-point bending test, in which the center of the fiber is deflected by a known force. We extend this technique by modeling the deflection measured at several points along a suspended fiber, allowing us to obtain more accurate data, as well as to justify the mechanical model used. As a demonstration, we have measured a value of 78 +/- 17 GPa for Young's modulus of bacterial cellulose fibers with diameters ranging from 35 to 90 nm. This value is considerably higher than previous estimates, obtained by less direct means, of the mechanical strength of individual cellulose fibers.     

Cleavage of X-H bonds (X = N, o, or C) by copper(I) alkyl complexes to form monomeric two-coordinate copper(I) systems

The monomeric copper(I) alkyl complexes (IPr)Cu(R) [R = Me or Et; IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene] react with substrates that possess N-H, O-H, and acidic C-H bonds to form monomeric systems of the type (IPr)Cu(X) (X = anilido, phenoxide, ethoxide, phenylacetylide, or N-pyrrolyl) and methane or ethane. Solid-state X-ray crystal structures of the anilido, ethoxide, and phenoxide complexes confirm that they are monomeric systems. Experimental studies on the reaction of (IPr)Cu(Me) and aniline to produce (IPr)Cu(NHPh) suggest that a likely reaction pathway is coordination of aniline to Cu(I) followed by proton transfer to produce methane and the copper(I) anilido complex.     

Synthesis and inverse electron demand Diels-Alder reactions of 3,6-bis(3,4-dimethoxybenzoyl)-1,2,4,5-tetrazine

The synthesis of 3,6-bis(3,4-dimethoxybenzoyl)-1,2,4,5-tetrazine (2) and the scope of its reactivity in inverse electron demand Diels-Alder reactions are disclosed representing the first systematic study of the [4 + 2] cycloaddition reactions of 3,6-diacyl-1,2,4,5-tetrazines.     

Synthesis of single-crystalline perovskite nanorods composed of barium titanate and strontium titanate

We report the solution-based synthesis of single-crystalline nanorods composed of barium titanate (BaTiO3) and strontium titanate (SrTiO3), which yields well-isolated nanorods with diameters ranging from 5 to 60 nm and lengths reaching up to >10 mum. Electron microscopy and diffraction measurements show that these nanorods are composed of single-crystalline cubic perovskite BaTiO3 and SrTiO3 with a principal axis of the unit cell preferentially aligned along the wire length. These BaTiO3 and SrTiO3 nanorods should provide promising materials for fundamental investigations on nanoscale ferroelectricity, piezoelectricity, and paraelectricity.     

Chemistry between magnesium and multiple molecules in tris(8-hydroxyquinoline) aluminum films

Metal organic contacts are at the basis of devices such as organic light emitting diodes (OLEDs). Here, we report a theoretical investigation of the chemical interaction between a Mg atom and an organic film made of tris(8-hydroxyquinoline)aluminum (Alq3) molecules. The latter is modeled either by an isolated molecule or by a bulk crystal. Using first-principles molecular dynamics for structural optimization, we find that an isolated Alq3 molecule and a Mg atom form an ion-pair. However, when the metal atom interacts with molecules in a bulk crystalline environment, we find that an organometallic complex is energetically preferred over the ion-pair. The complex formation is an effect of the environment which makes possible the interaction of the metal atom with several adjacent molecules. Here, our calculated O(1s) and N(1s) core level shifts agree well with recent experimental data on Alq3 films exposed to Mg. Our results resolve the apparent contradiction between experiment and predictions made in previous calculations in which a single Alq3 molecule was used to model a thin film.     

Metal-pentaborane(9) derivatives: 2-[Co(CO)4]B5H8 and 2[(η5-C5H5)Fe(CO)2]B5H8

Reaction of 2-XB₅H₈ (X  Cl, Br) with Naco(CO)₄ produces the transiently stable 2-[Co(CO)₄]B₅H₈. The similar 2-[(η⁵-C₅H₅)Fe(CO)₂]B₅H₈, which exhibits much greater thermal stability, is prepared by reaction of LiB₅H₈ with (η⁵-C₅H₅)Fe(CO)₂I. Reactions of CO₂(CO)₈ with B₅H₉ under a variety of conditions produce 2-[Co(CO)₄]B₅H₈ along with an inseparable impurity that appears to be 1-[Co(CO)₄]B₅H₈.