Diffusion in Lorentz lattice gas automata with backscattering

The probability of first return to the initial intervalx and the diffusion tensorD _x are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution. The same values forx andD _x apply also to a regular space lattice with a fraction of sites occupied by a scatterer in the limit of a small concentration of scatterers. If backscattering occurs, the results are very different from the Boltzmann approximation. The theory is applied to different types of lattices and different types of scatterers having rotational or mirror symmetries.     

Beiträge zur Chemie der Pyrrolpigmente, 70. Mitt.: Zum aktiven Transport mit tripyrrinoiden Liganden

The tripyrrin carboxylic acid6 exhibits a pronounced efficiency for carrier mediated proton driven secondary active transport (counter transport) for a series of toxic or valuable cations in a bulk chloroform membrane. In case of Zn⁺⁺ ions the mechanism including complete concentration profiles forNerst diffusion layers and bulk phase have been established. This compound might be used for detoxification or enrichment of precious metals using membrane separation systems.

Herrn Prof. Dr.A. Neckel mit den besten Wünschen zum 60. Geburtstag gewidmet.     

Solvent extraction and bulk liquid membrane transport of Co(II) and Ni(II) ammine cations by proton-ionizable crown ethers

Separation efficiencies and selectivities in solvent extraction of Co(II) and Ni(H) ammine cations from aqueous solutions into chloroform and toluene and in transport through bulk toluene membranes by proton-ionizable crown ethers have been determined. Six proton-ionizable crown ethers with differing lipophilicities, polyether cavity sizes and ionizable groups (carboxylic and sulfonic acid functions) were examined. Higher selectivity and efficiency for Co(II) ammine cation extraction was observed for the more lipophilic, proton-ionizable crown ethers. Highly lipophilic crown carboxylic acids provided effective and selective transport of Co(II) ammine cations through bulk toluene membranes.Presented in part at the 6th International Symposium on High Purity Materials in Science and Technology: Preparation, Characterization and Application of Well-Defined Materials, Dresden, GDR, May 1985, Poster D91, Poster Abstracts, pp. 144, 145.All extraction and transport experiments were conducted at this location.     

Electrical conduction nature and phase transition in CaTi1−x FexO3−δ (x = 0.1–0.5)

Transport numbers for oxygen ions and protons are measured by an emf method in the system CaTi_1?x Fe_xO_3?δ (x = 0.1–0.5) in the oxidizing and reducing atmospheres in the temperature interval 973–1173 K. It is shown that the compounds under study are mixed ion-electron conductors at small iron concentrations and electron conductors, at large iron contents. The proton conductivity in the compounds is very poor and does not exceed 0.5% in air. On the basis of the temperature dependences of transport numbers for ions and linear expansion, it is established that the CaTi_0.9Fe_0.1O_3?δ system has a phase transition of a second order in a reducing environment at 1020–1050 K. The total and partial electron conductivities of CaTi_0.9Fe_0.1O_3?δ are studied as a function of the partial pressure of oxygen at 1173 K. The nature of electroconduction in CaTi_1?x Fe_xO_3?δ is discussed.     

Beiträge zur Chemie der Pyrrolpigmente, 44. Mitt.: Gallenfarbstoffe als Ionophore

The carrier mediated transport of cations using model compounds of the verdinoid and rubinoid bile pigment structural type as ionophores is studied. Verdinoid bile pigments turn out to be very effective carriers for cations exhibiting a pronounced selectivity for certain transition metal ions like Cr^+-+, Fe⁺⁺, Cu⁺⁺ and Zn⁺⁺. The scope of this behaviour of verdinoid bile pigments is compared to [18]-crown-6 and meso-tetraphenylporphin and is discussed with regard to structural, biological, analytical and technical implications.

     

Diffusion in aqueous copper sulfate and copper sulfate-sulfuric acid solutions

Diffusion coefficients of copper sulfate-water and copper sulfate-sulfuric acid-water solutions have been determined at 25°C using conductimetric and diaphragm-cell techniques. The ternary diffusion measurements indicate that diffusion of sulfuric acid can produce large counterflows of copper sulfate and vice versa. If diffusion of copper sulfate in aqueous sulfuric acid solutions is treated as a binary process, the measured apparent diffusivities of copper sulfate can be 1 to 8% lower than the salt's true diffusivity. Equations are developed to predict transport coefficients from the concentrations and mobilities of the diffusing species.     

Synthetic receptors based on calix[4]arene functionalized at the lower rim in molecular recognition of dicarboxylic, α-hydroxycarboxylic,and α-amino acids

New calix[4]arenes, di- and tetrasubstituted at the lower rim, with different functional groups were synthesized. They were studied as carriers of a series of dicarboxylic and -hydroxycarboxylic acids through a liquid impregnated membrane. The calix[4]arenes under study are capable of molecular recognition of oxalic acid in the series of structurally similar dicarboxylic and -hydroxycarboxylic acids. The regularities found make it possible to change purposefully the receptor ability of 1,3-disubstituted calix[4]arenes by variation of the nature of substituents.     

An Analytical Study of Molecular Transport in a Zeolite Crystallite Bed

Analytical solutions of the diffusion equations to obtain the diffusant concentrations in the macro- and micropores which constitute the pore system of a zeolite bed are presented. The parameter which determines the influence of each pore type on the evolution of the adsorbate/adsorbant system towards the equilibrium state is described. Examples are given to illustrate a qualitative and quantitative study based on the curves obtained from these equations.     

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.