Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

Cis-Trans Isomerism in Square Planar [TeX 2 (stu) 2 ] Complexes (X = Br − , I − ) with Bulky Substituted Thiourea (stu) Ligands. Syntheses and Structures of Four New Tellurium(II) Complexes

The complexes were synthesised by adding a hot solution of the appropriate substituted thiourea in MeOH (Br m complexes) or DMF (I m complexes) to a solution of TeO 2 dissolved in hot conc. HCl. The structures of the resulting four-coordinate square planar complexes, cis -[TeBr 2 {( i PrNH) 2 CS} 2 ] ( 1 ), cis -[TeBr 2 {( i BuNH) 2 CS} 2 ] ( 2 ), trans -[TeI 2 {( i PrNH) 2 CS} 2 ] ( 3 ), and trans -[TeI 2 {( i BuNH) 2 CS} 2 ] ( 4 ), were studied by means of X-ray crystallographic methods. The average Te-S bond length in 1 and 2 is 2.5364 Å. The corresponding average Te-Br bond length is 2.9639 Å, reflecting the stronger trans influences of the two thioureas as compared to that of bromide. In 3 and 4 where there is no trans influence affecting the Te-ligand bonds, the average Te-S and Te-I bond lengths are 2.6926 and 2.9761 Å respectively. Tetraalkyl- or arylsubstituted thioureas alone as well as bulky disubstituted thioureas together with I m ligands seem to favor formation of trans complexes.     

Effective Relative Permeabilities and Capillary Pressure for One-Dimensional Heterogeneous Media

The paper presents an analytical construction of effective two-phase parameters for one-dimensional heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the interface between different rocks. The ensuing effective relative permeabilities and effective capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities.The applicability of the effective parameters in dynamic displacement situations is studied by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report computations studying the applicability of capillary limit parameters outside the strict limit.     

The multi‐stage centred‐scheme approach applied to a drift‐flux two‐phase flow model

For two‐phase flow models, upwind schemes are most often difficult do derive, and expensive to use. Centred schemes, on the other hand, are simple, but more dissipative. The recently proposed multi‐stage (MUSTA ) method is aimed at coming close to the accuracy of upwind schemes while retaining the simplicity of centred schemes. So far, the MUSTA approach has been shown to work well for the Euler equations of inviscid, compressible single‐phase flow. In this work, we explore the MUSTA scheme for a more complex system of equations: the drift‐flux model, which describes one‐dimensional two‐phase flow where the motions of the phases are strongly coupled. As the number of stages is increased, the results of the MUSTA scheme approach those of the Roe method. The good results of the MUSTA scheme are dependent on the use of a large‐enough local grid. Hence, the main benefit of the MUSTA scheme is its simplicity, rather than CPU ‐time savings. Copyright © 2006 John Wiley & Sons, Ltd.     

The short range expansion

Let V_i be short range potential and λ_i(ε) analytic functions. We show that the Hamiltonians H_ε = −Δ + ε⁻²∑_{i = l}ⁿλ_i(ε)V_i((· − x_i)/ε converge in the strong resolvent sense to the point interactions as ε → 0, and if V_i have compact support then the eigenvalues and resonances of H_ε, which remains bounded as ε → 0, are analytic in ε in a complex neighborhood of zero. We compute in closed form the eigenvalues and resonances of H_ε to the first order in ε.     

Chemical surface modifications of microfibrillated cellulose

Microfibrillated cellulose (MFC) was prepared by disintegration of bleached softwood sulphite pulp through mechanical homogenization. The surface of the MFC was modified using different chemical treatments, using reactions both in aqueous- and organic solvents. The modified MFC was characterized with fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM). Epoxy functionality was introduced onto the MFC surface by oxidation with cerium (IV) followed by grafting of glycidyl methacrylate. The length of the polymer chains could be varied by regulating the amount of glycidyl methacrylate added. Positive charge was introduced to the MFC surface through grafting of hexamethylene diisocyanate, followed by reaction with the amines. Succinic and maleic acid groups could be introduced directly onto the MFC surface as a monolayer by a reaction between the corresponding anhydrides and the surface hydroxyl groups of the MFC.     

A Novel Relative Permeability Model Based on Mixture Theory Approach Accounting for Solid–Fluid and Fluid–Fluid Interactions

A novel model is presented for estimating steady-state co- and counter-current relative permeabilities analytically derived from macroscopic momentum equations originating from mixture theory accounting for fluid–fluid (momentum transfer) and solid–fluid interactions (friction). The full model is developed in two stages: first as a general model based on a two-fluid Stokes formulation and second with further specification of solid–fluid and fluid–fluid interaction terms referred to as \(R_{{i}}\) (i =  water, oil) and R, respectively, for developing analytical expressions for generalized relative permeability functions. The analytical expressions give a direct link between experimental observable quantities (end point and shape of the relative permeability curves) versus water saturation and model input variables (fluid viscosities, solid–fluid/fluid–fluid interactions strength and water and oil saturation exponents). The general two-phase model is obeying Onsager’s reciprocal law stating that the cross-mobility terms \(\lambda _\mathrm{wo}\) and \(\lambda _\mathrm{ow}\) are equal (requires the fluid–fluid interaction term R to be symmetrical with respect to momentum transfer). The fully developed model is further tested by comparing its predictions with experimental data for co- and counter-current relative permeabilities. Experimental data indicate that counter-current relative permeabilities are significantly lower than corresponding co-current curves which is captured well by the proposed model. Fluid–fluid interaction will impact the shape of the relative permeabilities. In particular, the model shows that an inflection point can occur on the relative permeability curve when the fluid–fluid interaction coefficient \(I>0\) which is not captured by standard Corey formulation. Further, the model predicts that fluid–fluid interaction can affect the relative permeability end points. The model is also accounting for the observed experimental behavior that the water-to-oil relative permeability ratio \(\hat{{k}}_{\mathrm{rw}} /\hat{{\mathrm{k}}}_{\mathrm{ro}} \) is decreasing for increasing oil-to-water viscosity ratio. Hence, the fully developed model looks like a promising tool for analyzing, understanding and interpretation of relative permeability data in terms of the physical processes involved through the solid–fluid interaction terms \(R_{{i}}\) and the fluid–fluid interaction term R.     

Solar radiation, vitamin D and survival rate of colon cancer in Norway

Solar radiation contributes significantly to the status of serum calcidiol (25-hydroxyvitamin D3, 25-(OH)D3) in humans, even at the high latitudes of northern Norway. Thus, in late summer the serum concentration of calcidiol is roughly 50% larger than that in late winter, when the solar radiation in Norway contains too little ultraviolet radiation to induce any synthesis of vitamin D3 in human skin. This seems to influence the prognosis of colon cancer. We here report that the survival rate of colon cancer in men and women, assessed 18 months after diagnosis, is dependent on the season of diagnosis. A high serum concentration of calcidiol at the time of diagnosis, i.e. at the start of conventional therapy, seems to give an increased survival rate. This agrees with cell and animal experiments reported in the literature, as well as with epidemiological data from some countries relating colon cancer survival with latitude and vitamin D3 synthesis in skin. One possible interpretation of the present data is that, the level of calcidiol, or its derivative calcitriol (1alpha,25-dihydroxyvitamin D3, 1alpha,25-(OH)2D3), may act positively in concert with conventional therapies of colon cancer.     

Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations

Summary. We first analyse a semi-discrete operator splitting method for nonlinear, possibly strongly degenerate, convection-diffusion equations. Due to strong degeneracy, solutions can be discontinuous and are in general not uniquely determined by their data. Hence weak solutions satisfying an entropy condition are sought. We then propose and analyse a fully discrete splitting method which employs a front tracking scheme for the convection step and a finite difference scheme for the diffusion step. Numerical examples are presented which demonstrate that our method can be used to compute physically correct solutions to mixed hyperbolic-parabolic convection-diffusion equations. Received November 4, 1997 / Revised version received June 22, 1998     

Properties and characterization of hydrophobized microfibrillated cellulose

Microfibrillated cellulose (MFC) obtained by disintegration of bleached softwood sulphite pulp in a homogenizer, was hydrophobically modified by surface silylation with chlorodimethyl isopropylsilane (CDMIPS). The silylated MFC was characterized by Fourier transform infrared spectroscopy (FT-IR), atomic force microscopy (AFM), transmission electron spectroscopy (TEM), X-ray photoelectron spectroscopy (XPS) and white light interferometry (WLI). The degree of surface substitution (DSS) was determined using Si concentrations from XPS survey scans, as well as deconvoluted peaks in high-resolution C1s XPS spectra. The DSS values obtained by the two methods were found to be in good agreement. MFC with DSS between 0.6 and 1 could be dispersed in a non-flocculating manner into non-polar solvents, TEM observations showing that the material had kept its initial morphological integrity. However, when CDMIPS in excess of 5 mol CDMIPS/glucose unit in the MFC was used, partial solubilization of the MFC occurred, resulting in a drop in the observed DSS and a loss of the microfibrillar character of the material. The wetting properties of films cast from suspension of the silylated MFC were also investigated. The contact angles of water on the films increased with increasing DSS of the MFC, approaching the contact angles observed on super hydrophobic surfaces for the MFC with the highest degree of substitution. This is believed to originate from a combination of low surface energy and surface microstructure in the films.