Zintl‐Anionen des Siliciums in den Halogeniden La3Cl2Si3 und La6Br3Si7

Zintl Anions of Silicon in the Halides La₃Cl₂Si₃ and La₆Br₃Si₇ La₃Cl₂Si₃ and La₆Br₃Si₇ are prepared at temperatures of around 950 °C from LaX₃ (X = Cl, Br), La metal and Si as starting materials. La₃Cl₂Si₃ crystallizes in C2/m with a = 1802(3), b = 420.6(4), c = 1058(2) pm, β = 97.9(2)°, and La₆Br₃Si₇ in Pmmn mit a = 1686.9(2), b = 412.93(11), c = 1185.2(1) pm. In both compounds the Si atoms are located in trigonal prisms of La atoms, which are connected through common triangular and rectangular faces to form layers. The bromine atoms connect the metal atom double layers. In La₃Cl₂Si₃ the Si atoms form zig‐zag chains, in La₆Br₃Si₇ chains build up from ‐connected Si₁₂ rings. Both compounds are metallic conductors.     

Chain direction elastic modulus of PE crystal and interlamellar force constant of n-alkane crystals from RAMAN measurements

Spectroscopic data can deliver force constants only if the exact chain conformation is known. For the longitudinal acoustic modes (LAM), however, simple linear chain models can be used to yield the effective longitudinal chain modulus from spectroscopic data of oligomer crystals. The model of p-coupled linear chain molecules with N masses and only nearest neighbor interactions was used to investigate the longitudinal acoustic modes with s nodes. The frequencies plotted versus s/N fall onto different branches for different s. The intermolecular coupling and the heavier endmasses shift the LAM branches to higher and lower frequencies, respectively. There exists a value x₀ depending on the masses and force constants, where the branches cut the dispersion curve of the infinite molecule. For s/N ≥ x₀ the effect of endmasses dominates. Low-frequency RAMAN spectra of n-alkanes (N = 20, …, 40 C atoms) were recorded and analyzed. The LAM1 branch runs clearly above a smooth fit through all other LAM data and the origin. This fit approximates to first order the dispersion curve of the infinite PE molecule in an ideal crystal. Its curvature exceeds that of the dispersion curve of the simple linear chain, but is somewhat smaller than that of the dispersion curve of the planar zig-zag chain with rigid bonds. The slope at the origin yields the limiting elastic modulus E_c = 315 GPa in chain direction of crystalline polyethylene. From our measurements on n-alkanes we obtained the frequency shift of LAM1 due to the interlayer coupling and the heavier endmasses. Calculation of the intermolecular coupling constant of the model of a long row of linear chain molecules with the same frequency shift yield the mean value f_l = 2.5 N/m. This value decreases with increasing chain length. The relevance and applicability of the model is discussed. © 1997 John Wiley & Sons, Inc.     

Single-ion and salt conductor polymer electrolytes based on poly(4-vinylpyridine) quaternized with poly(ethylene oxide) side chains

A new type of single-ion conductor with fixed cation was synthesized by spontaneous anionic polymerization of 4-vinylpyridine in the presence of short polyethylene oxide ( PEO ) chains as alkylating agents. These comblike polymers have low T_gs and are amorphous with the shorter PEO s. Their conductivities are unaffected by the nature of the anion ( Br ⁻, ClO ₄⁻, and tosylate) and are controlled by the free volume and the mobility of the pendant cation. By comparison of the results at constant free volume, it is shown that the charge density decreases with the increasing length of pendant PEO demonstrating that PEO acts only as a plasticizing agent. Best conductivity results (σ = 10⁻⁵ S cm⁻¹ at 60°C) are obtained with PEO side chains of molecular weight 350. With this sample, the conductivity in the presence of various amounts of added salt (LiTFSI) was studied. A best value of 10⁻⁴ S cm⁻¹ at 60°C is obtained with a molar ratio EO/Li of 10. It is shown that, over the range of examined concentrations (0.2–1.3 mol Li kg⁻¹), the reduced conductivity σ_r/c increases linearly with increasing salt concentration showing that the ion mobility increases continuously. Such behavior is quite unusual since in this concentration range a maximum is generally observed with PEO systems. To interpret this result and by analogy with the behavior of this type of polymer in solution, it is proposed that the conformation of these polymers in the solid state is segregated with the P4VP skeleton more or less confined inside the dense coils surrounded by the PEO side chains. Under the influence of the increasing salt concentration, this microphase separation vanishes progressively: The LiTFSI salt exchanges with the tosylate anions and acts as a miscibility improver agent. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2719–2728, 1997     

Curing theory of A_f-A_g type free radical polymerization (Ⅱ)——Characterization of network structural parameters

By means of the polymer statistical theory, the A_f-A_g type nonlinear free radical polymerization is investigated to give the number of effective elastic chains, the number of effective elastic mers and the average length for the elastic chains. The corresponding quantities for the dangling chains, the number of effective cross-linkage and the modulus are also obtained. Furthermore, the number- and weight-fractions of elastic chains are deduced.     

Electrodeless Piezoelectric Quartz Crystal Sensor for Determination of Total Urinary Reducing Sugar

A glucose-sensing system was developed in which an electrodeless piezoelectric quartz crystal was used to measure mass changes on the surface of a quartz plate during the reduction of Ag(NH₃)⁺₂ by glucose. A satisfactory correlation was obtained between the frequency shift and the glucose concentration in the range 1.0–25 mM, and the total reducing sugar in urine was determined. Treatment with 8 M nitric acid after each measurement was effective for cleaning the quartz surface, and the electrodeless piezoelectric quartz crystal sensor possessed excellent reproducibility and reusability during repeated use over 400 times. For the determination of total reducing sugar in urine (or blood), the present method can avoid the interferences occurring in a colorimetric method such as the color and turbidity of clinical specimens.     

Flabby sheaves of chains for singular homology

Iterating the barycentric subdivision operator in a singular complex, we construct flabby sheaves of chains for singular homology. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 396–401, March, 1999.     

Block Two-stage Methods for Singular Systems and Markov Chains

The use of block two-stage methods for the iterative solution of consistent singular linear systems is studied. In these methods, suitable for parallel computations, different blocks, i.e., smaller linear systems, can be solved concurrently by different processors. Each of these smaller systems are solved by an (inner) iterative method. Hypotheses are provided for the convergence of non-stationary methods, i.e., when the number of inner iterations may vary from block to block and from one outer iteration to another. It is shown that the iteration matrix corresponding to one step of the block method is convergent, i.e., that its powers converge to a limit matrix. A theorem on the convergence of the infinite product of matrices with the same eigenspace corresponding to the eigenvalue 1 is proved, and later used as a tool in the convergence analysis of the block method. The methods studied can be used to solve any consistent singular system, including discretizations of certain differential equations. They can also be used to find stationary probability distribution of Markov chains. This last application is considered in detail.     

Green's Function Theory of Linear Magnetic Chains with Anisotropic Coupling

The one-dimensional spin-1/2 ferromagnetic and antiferromagnetic chains with anisotropic coupling are studied within the Green's function theory in both planar and uniaxial regimes. The spin Green's functions are decoupled at a stage one-step further than the Tyablikov's decoupling under the constraint 2>= 0. The behaviors of the correlation functions are studied in the entire temperature regime. The thermodynamic properties are also discussed, and the result is consistent with the numerical simulation.     

CuClSe1.53Te0.47 and CuClSe0.56Te1.44: Structural and Vibrational Spectroscopic Investigations on Copper(I) Chalcogen Chlorides

CuClSe_1.53Te_0.47 and CuClSe_0.56Te_1.44 are obtained from the reaction of CuCl, Se, and Te in stoichiometric amounts. Both copper(I) selenium tellurium chlorides are monoclinic, space group P2₁/n (no. 14) with lattice constants of a = 7.837(1) Å, b = 4.699(1) Å, c = 10.762(2) Å, β = 104.37(2)°, V = 383.9(1) ų (CuClSe_1.53Te_0.47), and a = 8.074(1) Å, b = 4.830(1) Å, c = 10.973(1) Å, β = 103.87(2)°, V = 415.5(1) ų (CuClSe_0.56Te_1.44), and Z = 4. A common feature of these isostructural compounds are heteroatomic strands [YY'] (Y, Y' = chalcogen). These strands are running along [010] and are connected to layers by chains [CuCl]. Vibrational spectra of CuClSe_1.53Te_0.47, CuClSe_0.56Te_1.44, CuXTe₂ and CuX'Se₂ (X = Cl, Br, I; X' = Cl, Br) are analysed with respect to the bonding relations of the chalcogen chains. Modes derived from IR and Raman spectra are assigned by correlation with tri gonal Se and related copper(I) chalcogen halides. Both, X‐ray structural data and an analysis of the chalcogen vibrational modes in IR and Raman spectra, lead to a detailed insight into the ordering phenomena of the chalcogen chains in this type of copper(I) chalcogen halides.