Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

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.     

Beiträge zur Chemie der Pyrrolpigmente, 78. Mitt.: Die Eigenschaften desb-Nor-bilatrien-abc-b-Nor-biladien-ac-Systems

The redox coupleb-nor-biladiene-ac (2)/b-nor-bilatriene-abc (3) exhibits an oxidative half wave potential of 800 mV in acetonitrile solution. It is demonstrated that it can be used as an extremely efficient electron carrier through bulk membranes. Whereas2 is not suitable as a ligand in carrier mediated cation transport,3 is a medium suited carrier for Cu(II) or Zn(II) ions, however, it is the most efficient one found so far for transport of Hg(II) ions. A 1:1 zinc chelate of3 is isolated and characterized. it is deduced to represent a polymer consisting of about 73 monomer units.

     

Improvement of the performance of facilitated transport membrane process through nonuniformity

Facilitated transport process has attracted much attention because high selectivity and high permeability may be achieved. However, most research on facilitated transport process is concerned only with uniform membranes. In this paper, a model predicting the gas separation performance of a hollow-fiber module with facilitated transport membrane is developed. The influence of feed rate, operation pressure, and permeant-feed flow pattern on the module performance are analyzed and the effect of the nonuniform distribution of reaction equilibrium constant is examined. The calculated results show that the nonuniform active distribution may cause an improved module performance. Because of the passive transport characteristics of the facilitated transport process, the mass transfer driving force across the membrane has a great influence on the improvement of the module performance through a facilitated transport effect.     

Mass transfer determining parameter in facilitated transport through di-(2-ethylhexyl) dithiophosphoric acid activated composite membranes

Activated composite membranes (ACMs) containing di-(2-ethylhexyl) dithiophosphoric acid (D2EHDTPA) as a carrier have been found to facilitate the transport and separation of several cations. This paper describes an approach to the chemical characterisation of the transport phenomena of Zn²⁺, Cd²⁺, Cu²⁺, Ni²⁺, Sn²⁺ and In³⁺ by an ACM. The selectivity of D2EHDTPA based ACM towards different metal ions is presented and discussed focusing in Zn²⁺ and Cd²⁺ transport and recovery. Selectivity demonstrates that zinc ions are removable from mixtures due to the different extraction strength of D2EHDTPA. Such selectivity is based on the differences of the dynamic behaviour of the metal ions transport. In addition, a correlation of the chemical behaviour of those ACM systems with the corresponding solvent extraction systems has been found.     

Effect of pressure on retention factors in HPLC using a non-porous stationary phase

Summary Pressure and temperature have significant influence on retention in HPLC. This study investigates the effect of pressure and temperature on the retention behavior of aromatic hydrocarbons (toluene, ethyl benzene, butyl benzene, pentyl benzene) and polar, acidic and basic samples (phenol, acetophenone, N,N-dimethyl aniline, benzophenone) on a reversed phase column. The effect has been studied on non-porous, tetradecyl (C₁₄) coated silica particles. We found that the adsorption-induced decrease of the partial molar volume of the solutes investigated was between ΔV _m =5–15 cm³ mol⁻¹. The increment of the decrease of the partial molar volume due to the addition of one CH₂ group, for the homologous series of the aromatic hydrocarbons is approximately ΔV _CH2 =2.3 cm³mol⁻¹. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001.     

Conduction and Transport Numbers in Metacomposites MeWO<Subscript>4</Subscript> ⋅ WO<Subscript>3</Subscript> (Me = Ca,Sr, Ba)

The conduction and transport numbers of charge carriers for composites in the systems MeWO₄-WO₃ (Me = Ca, Sr, Ba) are studied as a function of the temperature and the activity of oxygen in a gas phase. The transport numbers are determined by an emf method and are estimated from dependences of conductance on the activity of oxygen in a gas phase. The deficiencies of the given procedure as applied to investigation of properties of composite phases are analyzed. The materials under study are classified with a class of metacomposites. The concentration intervals of the ionic, mixed, and electronic conductions are determined. The conduction of composites of compositions (100 − x)MeWO₄ ⋅ xWO₃ is predominantly ionic at x ≤ 10 (Me = Ca), x ≤ 60 (Me = Sr), and x ≤ 45 (Me = Ba). The obtained data are explained in the framework of a model that represents a composite as a distributed matrix system where a film of surface phase MeW-s with a high mobility of oxygen ions plays the role of a connected matrix. It is presumed that the surface phase MeW-s possesses double-sided surface activity (α _MeW-s ≤ ) and a higher mobility with respect to MeWO₄ and WO₃. The discovered anomalies of dependences (T) and partial dependences , σ_el(T) are explained by a change in the stoichiometry, morphology, and the degree of connectedness of surface phase MeW-s caused by with a change in the temperature and composition of composites.__________Translated from Elektrokhimiya, Vol. 41, No. 6, 2005, pp. 680–693.Original Russian Text Copyright © 2005 by Neiman, Pestereva, Sharafutdinov, Kostikov.Published on the basis of a report delivered at the VII Meeting on Fundamental Problems in Solid-State Ionics (Chernogolovka-2004).     

Ternary rare-earth nickel arsenides R3Ni7As5 (R=La, Ce, Pr, Nd, Sm) with a new variant of the BaAl4-type: crystal structure and physical properties

The ternary rare-earth nickel arsenides R₃Ni₇As₅ (R=La, Ce, Pr, Nd, Sm) were prepared by arc melting the elemental components and subsequent annealing at T=1070 K. The crystal structure of Ce₃Ni₇As₅ was determined from single-crystal X-ray data: space group Pmmn, Z=2; a=1.24210(6), b=0.40797(2), c=0.96436(5) nm, R_F=0.037 (R_w=0.044); 596 independent reflections; 53 variable parameters. It is a new structure type, which belongs to the family of BaAl₄-related structures. The magnetic properties are as follows: La₃Ni₇As₅ is a Pauli-type paramagnet above 4.2 K, Pr₃Ni₇As₅ remains paramagnetic in the temperature range investigated and Nd₃Ni₇As₅ undergoes a ferromagnetic ordering at T_C=24 K. Sm₃Ni₇As₅ orders antiferromagnetically at a Néel temperature of T_N=18 K followed by a spin flip towards parallel spin-alignment below T_C=6 K. Ce₃Ni₇As₅ reveals a strong deflection of the linear temperature dependence of the inverse susceptibility due to an intermediate valence behavior. The temperature dependence of the electrical resistivities for the La, Pr, Nd, Sm containing samples corroborates with the metallic state of the non-magnetic (La) and the magnetically ordered compounds, whereas in case of Ce₃Ni₇As₅ the resistivity seems to be determined by an interplay of Kondo scattering and crystalline field effects. L_III X-ray absorption spectra confirm the demagnetization effects owing from valence fluctuations, the actual valence thereby changes from ν=3.10-3.14 at room temperature and 10 K, respectively.     

Investigations on Chemical Vapour Transport of Intermetallic Phases in the System Co/Fe/Si

The ternary phases existing on the quasi binary section CoSi/FeSi and CoSi₂/β‐FeSi₂ have been investigated by solid state reactions and chemical transport. The solid solution serie Co_xFe_1‐xSi can be described as a regular solution. The transport behaviour calculated is in good agreement with the experiments. The phases have been characterized by X‐ray powder diffraction, EDX and ICP‐OES. The temperature dependence of the resistivity has been measured from 20 K up to room temperature on single crystals.