Transport properties of the Lorentz gas: Fourier's law

We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT ₁ andT ₂ respectively,T ₁ <T ₂. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL ¹-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T ₂-T ₁)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship.     

Studies on tetra-amine phthalocyanines

Metal(II) tetranitro phthalocyanines of cobalt, nickel and copper are synthesized in pure state by a novel modified method. The complexes are characterized using elemental, electronic and IR spectral studies. Pure metal(II) tetra-amino phthalocyanines of cobalt, nickel and copper are synthesized by reducing the nitro groups of the above complexes using sodium sulphide. These complexes are also characterized by elemental, electronic, IR spectral and magnetic susceptibility measurements. The nature of the electrical conductivities of the above three metal(II) tetra-amino phthalocyanine derivatives are studied in the temperature range 303-473 K and the data are presented. Among the effect of various substituent groups on the electrical conducting property of phthalocyanine, amine group substituent on the peripheral benzene ring of the phthalocyanine molecule has been found to increase electrical conductivity to a greatest extent. These complexes showed about 10⁵-10⁶ times higher electrical conductivities compared to their parent phthalocyanine compounds.     

Synthesis, crystal structures and ionic conductivities of Bi14P4O31 and Bi50V4O85. Two members of the series Bi18−4mM4mO27+4m (M=P, V) related to the fluorite-type structure

The two hitherto unknown compounds Bi₁₄P₄O₃₁ and Bi₅₀V₄O₈₅ were prepared by the direct solid-state reaction of Bi₂O₃ and (NH₄)H₂PO₄ or V₂O₅, respectively. Bi₁₄P₄O₃₁ crystallizes in a C-centred monoclinic symmetry (C2/c space group) with the unit-cell parameters: , , and β=93.63(1)° (Z=16). The symmetry of Bi₅₀V₄O₈₅ is also monoclinic (I2/m space group) with lattice parameters of , , and β=90.14(1)° (Z=2). Both structures correspond to a fluorite-type superstructure where the Bi and P or V atoms are ordered in the framework. An idealized structural model is proposed where the structures result of the stacking of mixed atomic layers of composition [Bi₁₄M₄O₃₁] and [Bi₁₈O₂₇] respectively. This new family can be formulated Bi_18−4mM_4mO_27+4m with M=P, V and where the parameter m (0?m?1) represents the ratio of the number of [Bi₁₄M₄O₃₁] layers to the total number of layers in the sequence. Bi₁₄P₄O₃₁ corresponds to m=1 when Bi₅₀V₈O₈₅ corresponds to m=1/3. In this last case, the structural sequence is simply one [Bi₁₄V₄O₃₁] layer to two [Bi₁₈O₂₇] layers. As predicted by the proposed structural building principle, Bi₁₄P₄O₃₁ is not a good ionic conductor. The conductivity at 650 °C is 4 orders of magnitude lower from those found in Bi₄₆M₈O₈₉ (M=P, V) (m=2/3) and Bi₅₀V₄O₈₅ (m=1/3).     

Neue ternäre Käfigverbindungen aus den Systemen Barium–Indium/Zink/Cadmium–Germanium: Zintl-Verbindungen mit Phasenbreite?

New Ternary Clathrate Compounds in the Systems Barium–Indium/Zinc/Cadmium–Germanium: Zintl Compounds with Phase Width? By systematic investigations in the systems barium–indium/zinc/cadmium–germanium we found a couple of new electrovalent ternary compounds with A₈X₄₆ clathrate (I) type structures. They crystallize cubically in space-group Pm3n. For Ba₈In₁₆Ge₃₀ (a = 1 075.8 pm), Ba₈Zn₈Ge₃₈ (a = 1 082.0 pm) and Ba₈Cd₈Ge₃₈ (a = 1 096.0 pm) the structures were verified by X-ray single crystal diffraction data. According to valence and bounding distances the new clathrates should be Zintl compounds. Measurements of the temperature dependence of the electrical resistivity proved, that they are indeed semiconductors. A part of the 2B/3B metal atoms can be substituted by germanium. Charge balance will be retained by creation of vacancies in the A₈X₄₆ type structures. By phase analysis the limits of the composition range were determined as Ba₈In₄Ge₉[]₃Ge₃₀ (a = 1 084.9 pm), Ba₈Zn₄Ge₁₀[]₂Ge₃₀ (a = 1 073.6 pm) and Ba₈Cd₄Ge₁₀[]₂Ge₃₀ (a = 1 082.0 pm).     

Synthesis and property of soluble poly(1,1′-dialkyl-3,3′-ferrocenylenevinylene)s via titanium-induced dicarbonyl-coupling reaction of 1,1′-dialkylferrocene-3,3′-dicarbaldehydes

1,1′-Dialkylferrocene-3,3′-dicarbaldehydes ( 1a–c ) with long alkyl chains such as ethyl, hexyl, and dodecyl groups were prepared in 13–25% yield via three-step reactions. The titanium-induced dicarbonyl-coupling reaction of 1a–c gave poly(1,1′-dialkyl-3,3′-ferrocenylenevi-nylene)s ( 2a–c ) in quantitative yields, which were the molecular weights of 3000–10,000 and highly soluble in chloroform, benzene, and hexane. The electrical conductivity and the third-order nonlinear optical susceptibility for poly(1,1′-dihexyl-3,3′-ferrocenylenevinylene) ( 2b ) were estimated to be 1 × 10^?2 S/cm on doping with iodine and 1–4 × 10^?12 esu at a wavelength of 1–2.4 μm, respectively. © 1995 John Wiley & Sons, Inc.     

Synthesis and characterization of P2O5–SiO2–X (X = phosphotungstic acid) glasses as electrolyte for low temperature H2/O2 fuel cell application

A new class of proton conducting glass membranes for hydrogen fuel cell applications are being developed using phosphotungstic acid. These glasses are being design to yield high proton conductivities could be potential substitutes for electrolytes in H₂/O₂ fuel cell. P₂O₅–SiO₂–PWA glasses have been non-crystalline phases confirmed by structural studies. The glass materials showed good mechanical and thermal stability, and also found a maximum proton conductivity of 9.1 × 10⁻² S/cm at 90 °C and 30% RH. The average pore size less than 5 nm was determined by Barrett–Joyner–Halenda (BJH) desorption method. The electrochemical activity was investigated by polarization curves and current–voltage profiles. A maximum power density value of 10.2 mW/cm² was obtained using 0.15 mg/cm² of Pt/C loaded on electrode and 5P₂O₅–87SiO₂–8PWA glasses at 30 °C and 30% humidity.     

Optimization of an electrolytic conductivity detector for determination of toxic nitrogen-containing food contaminants separated by open tubular column gas chromatography

The combination of open tubular column gas chromatography with electrolytic conductivity detection has been evaluated for the determination of nitrogen-containing pesticide residues in food extracts. Optimization of the column position at the column-detector interface was crucial to the successful operation of the detector. The signal-to-noise ratio and response stability of the detector are greatly influenced by the composition of the electrolyte solvent. Large volume splitless injections using retention gaps and optimized detector operating conditions enabled pesticide residues in food extracts to be determined at sub parts-per-million levels. Although the electrolytic conductivity detector is less sensitive than the thermionic ionization detector, its greater nitrogen selectivity can he crucial to the determination of nitrogen-containing contaminants in food extracts, particularly in complex mixtures where phosphorus-containing contaminants or matrix compounds are also present.     

Structural and Transport Properties of Mg1−xMnxMn2O4±δ Spinels

The synthesis and structural properties of Mg_1−xMn_2+xO₄, for 0≤x≤1 are described. Complete miscibility in the solid state exists for this system. For the material with the correct stoichiometry, i.e. MgMn₂O₄, the effect of temperature on the cation distribution was investigated= above 600°C the inversion degree (m) starts increasing. The electrical conductivity shows a small dependence on P(O₂) which is consistent with the small oxygen non-stoichiometry determined by means of thermogravimetry. The main contribution to the transport properties arises from the inversion equilibrium. Two distinct conductivity regimes, below and above the inversion threshold, can be assumed to explain the electrical conductivity and thermoelectric power results.     

Contributions on the Properties of Titanates with Ilmenite Structure. IV. The effect of an order-disorder transition on the high temperature electrical conductivity of NiTiO3

NiTiO₃ shows an order-disorder transition from an ordered ilmenite structure to a corundum structure at high temperatures. The transition is followed by a strong increase of the specific electrical conductivity. The conductivity was investigated as a function of temperature and oxygen activity. An order parameter according to common phase transition theories can be used to describe the behaviour of the conductivity in the transition region and vice versa. A model for the defect structure of NiTiO₃ is presented.     

Natural zeolitic material of the clinoptilolite type doped with iodine and its ions

The aim of this study was the preparation of natural zeolitic materials doped with iodine and its ions. Natural zeolite from an East Slovakian deposit was used. The content of iodine in the zeolitic products depended on the experimental conditions used for the preparation. The products and their intermediates obtained at 100, 200, 400 and 900°C were identified.