Polyferrocenylsilane microspheres: synthesis,mechanism of formation,size and charge tunability,electrostatic self-assembly,and pyrolysis to spherical magnetic ceramic particles

Pt(0)-catalyzed ring-opening precipitation copolymerization of [1]silaferrocenophanes fcSiMe(2) (3) and the spirocyclic cross-linker fcSi(CH(2))(3) (4) (fc = Fe(eta(5)-C(5)H(4))(2)) was used to prepare polyferrocenylsilane microspheres (PFSMSs) under mild conditions. By varying the reaction conditions, a wide variety of other morphologies was obtained. The effects of temperature, monomer ratio, solvent composition, catalyst concentration, and time on the observed morphology were investigated and interpreted in terms of a mechanism for microsphere formation. The most well-defined particles were formed using equimolar amounts of 3 and 4, in a 50:50 mixture of xylenes and decane at 60 degrees C with gentle agitation. Chemical oxidation of the polymeric microspheres led to positively charged particles (OPFSMSs) which underwent electrostatically driven self-assembly with negatively charged silica microspheres to form core-corona composite particles. Redox titration with controlled amounts of the one-electron oxidant [N(C(6)H(4)Br-p)(3)][PF(6)] in acetonitrile led to the oxidation of the outer 0.15 microm (ca. 32%) of the PFSMSs. The resulting OPFSMSs were reduced back to their neutral form by reaction with hydrazine in methanol. Pyrolysis of the PFSMSs led to spherical magnetic ceramic replicas with tunable magnetic properties that organize into ordered 2-D arrays at the air-water interface under the influence of a magnetic field.     

CPT violation implies violation of Lorentz invariance

A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.     

The Relation of Constraints on Particle Statistics for Different Species of Particles

Quons are particles characterized by the parameter q, which permits smooth interpolation between Bose and Fermi statistics; q = 1 gives bosons, q = -1 gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form ffb, where f is fermion-like and b is boson-like. We show that q _f ² = q_b. In particular, we relate the bound on q for photons to the bound on q_e for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to a high precision.     

A fully automatic method for predicting internal reacting flows

A fully automatic method for computing elliptic internal reacting flows is presented. It uses a majorant operator-splitting method for the conservation of species equations, which permits their usually problematic integration to be performed in a two-step process. For the first nonreacting stage the algorithm of Gosman et al. [18] is utilised, whilst the form of the second reacting stage enables the method of characteristics to be implemented so that a set of ordinary differential equations is obtained. The latter are solved using Gear's [5] method for combatting the stiffness that is frequently associated with problems involving realistic chemical kinetic schemes. Some sample results for turbulent reacting flow in a combustor with a conical burner tunnel section demonstrate the viability of the technique.     

Enolstannanes as electrofugal groups in allylic alkylation

Enolstannanes serve as nucleophiles towards allylic acetates under the influence of palladium(O) catalyst.     

Global solutions of the Boltzmann equation on a lattice

The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.Supported by National Science Foundation Grant ENG-7515882.     

The conditional entropy in the microcanonical ensemble: The quantum lattice

The existence of the conditional entropy in the thermodynamic limit for a class of long range compatible observables operating on a quantum lattice is exhibited for the microcanonical ensemble. This limit is demonstrated first along a special sequence of cubes with a fixed contraction parameter. Properties of the parameter dependent limit are utilized to remove the parameter, and the results are extended to van Hove sequences approximable by cubes.