Statistical mechanics of bilayer membrane with a fixed projected area

The equilibrium and fluctuation methods for determining the surface tension, sigma, and bending modulus, kappa, of a bilayer membrane with a fixed projected area are discussed. In the fluctuation method the elastic coefficients sigma and kappa are measured from the amplitude of thermal fluctuations of the planar membrane, while in the equilibrium method the free energy required to deform the membrane is considered. The latter approach is used to derive new expressions for sigma and kappa (as well as for the saddle-splay modulus), which relate them to the pair-interactions between the amphiphiles forming the membrane. We use linear response theory to argue that the two routes lead to similar values for sigma and kappa. This argument is confirmed by Monte Carlo simulations of a model membrane whose elastic coefficients are calculated using both methods.     

Gel routes to environmental catalysts

Various methods for the preparation of metal oxide catalysts for environmental control purposes are described. These include coprecipitation, sol-gel, and impregnation, and are used to prepare mixed oxide catalysts of the types SnO₂-MO₂ (M=Ce or Zr), SnO₂-Ln₂O₃ (Ln = lanthanide), Ln-doped CeO₂, Cr (VI)-doped SnO₂, and Cu(II)-doped SnO₂. The aggregation in stable colloidal sols of SnO₂, CeO₂ and ZrO₂ is dependent on the concentration of the metal oxide. Techniques for the characterisation of these catalyst materials include gas adsorption, X-ray diffraction, and TEM/EDXA.     

Rotational and vibrational temperatures of naphthalene in a naphthalene-argon supersonic jet

In the $\text{A}$¹B_2u-$\text{X}$¹A_g system of naphthalene in a supersonic jet, rotational contour calculations show rotational temperatures of 2–60 K for argon carrier gas pressures of 1520-120 Torr. The b_1u vibration v₂₄ shows a high vibrational temperature which corresponds to the seeding temperature for pressures <400 Torr.     

An algorithm for semi-empirical design of nucleation rate surface

During the last half of century, Classical Nucleation Theory (CNT) has been developed and there have been advances in the molecular theory of nucleation. Most of these efforts have been directed towards small molecule system modeling using intermolecular potentials. Summarizing the nucleation theory, it can be concluded that the current theory is far from complete. Agreement is generally not obtained between experimental and theoretical results. In practical applications, parametric theories can be used for the systems of interest. However, experimental measurements are still the best source of information on nucleation. Experiments are labor intensive and costly, and thus, it is useful to extend the value of limited experimental measurements to a broader range of nucleation conditions. The available nucleation parameters represent only small regions of possible nucleation conditions over the range from the critical temperature to absolute zero. Thus, it is useful to develop better tools to use the data to estimate semi-empirical nucleation rate surfaces. Following our published approach, the nucleation rate surface for any system can be constructed over its phase diagram. This concept involves using the phase equilibrium diagram to establish lines of zero nucleation rates. Nucleation rate surfaces arise from equilibrium lines and their extensions that are representing unstable equilibria. Only limited experimental data is available for use in normalizing the slopes of the linearized nucleation rate surfaces. The nucleation rate surface is described in terms of steady-state nucleation rates. To design the surfaces of nucleation rates, several assumptions are presented. In the present study, an algorithm for the semi-empirical design of nucleation rate surfaces is introduced. The topology of the nucleation rate surface for a unary system using the example of water vapor nucleation is created semi-empirically. The nucleation of two concurrent (stable and unstable) phase states of critical embryos is considered in the context of multi-surface nucleation rates. Only one phase transition (melting) in the condensed state of water is considered for simplicity. The nucleation rate surface is constructed numerically using the available experimental results for vapor nucleation and phase diagram for water. The nucleation rate for water vapor is developed for the full temperature interval, i.e. from critical point to absolute zero. The results help to suggest a new direction for experimental nucleation research.     

Construction of orbital angular momentum eigenfunctions for many-particle systems by harmonic projection

Formulas are derived which allow the direct construction of total orbital angular momentum eigenfunctions for many-particle systems without the use of Clebsch–Gordan coefficients. One of the equations is closely analogous to Dirac' identity for the total spin operator. This equation describes the action of L² on a function of the particle coordinates in terms of a class operator of the symmetric group and a "contraction operator." A general projection operator for constructing symmetric eigenfunctions of L² is presented.     

A spirocyclic system comprising both phosphazane and phosphazene rings

The reaction of hexakis(cyclohexylamino) cyclotriphosphazene [NP(CyNH)(2)](3), 1, with phosphorus trichloride yields [NP(CyN)(2)PCl](3), 2, which contains three four-membered phosphazane rings fused in spirocyclic fashion to a central six-membered phosphazene ring and constitutes the first structurally characterized compound that comprises both phosphazene and phosphazane rings. The peripheral P atoms feature stereoactive lone pairs, and, thus, 2 exists in isomeric C(3h) and C(s) forms. The spirocyclic phosphazene-phosphazane derivative 2 carries three reactive PCl functions in peripheral positions, promising an interesting precursor molecule for the synthesis of extended phosphorus nitrogen structures of high rigidity. Extension of the PN moiety can be achieved by reaction of 2 with a primary amine yielding [NP(CyN)(2)PN(H)(t)Bu](3), 3, which features a central scaffold of 6 phosphorus and 12 nitrogen centers and aggregates via N-H...P hydrogen bonds in the solid state. On the contrary, the reaction of 1 with SbCl(3) undergoes incomplete proton abstraction, resulting in the formation of the tricyclic compound N(3)P(3)(CyNH)(4)(CyNSbCl(2))(2), 4, which contains two four-coordinate Sb centers chelated by N(exo)-N(ring) sites of the phosphazene.     

Synthesis of the Deuterium Labeled Isoflavone-<Emphasis Type="Italic">O</Emphasis>-glucoside 8,3′,5′-D<Subscript>3</Subscript>-Daidzin

The regio- and stereospecific glycosylation of 8,3′,5′-trideuterodaidzein 1 with α-acetobromoglucose to provide 8,3′,5′-trideuterodaidzein-7-O-β-glucopyranoside 2 is presented.     

Determination of internuclear distances in uniformly labeled molecules by rotational-resonance solid-state NMR

Rotational-resonance magic-angle spinning NMR experiments are frequently used to measure dipolar couplings and to determine internuclear distances. So far most measurements were performed on samples containing isolated spin pairs. Thus, extensive structure elucidation, for example in biomolecules, requires the preparation of a whole set of doubly labeled samples. Here, we describe the analysis of the rotational-resonance polarization-exchange curves obtained from a single, uniformly labeled sample. It is shown experimentally that, at a magnetic field of 14.09 T, the rotational-resonance conditions in uniformly (13)C-labeled threonine are sufficiently narrow to permit the measurement of five distances between the four carbon spins with an accuracy of better than 10%. The polarization-exchange curves are analyzed using a modified two-spin model consisting of the two active spins. The modified model includes an additional offset in the final polarization, which comes from the coupling to the additional, passive, spins. The validity of this approach is experimentally verified for uniformly (13)C-labeled threonine. The broader applicability of such a model is demonstrated by numerical simulations which quantify the errors as a function of the most relevant parameters in the spin system.