Two Algorithms for Computing the Randles–Sevcik Function from Electrochemistry

We derive two expansions of the Randles–Sevcik function : an asymptotic expansion of for x and its Taylor expansion at any x ₀ . These expansions are accompanied by error bounds for the remainder at any order of the approximation.     

An <Emphasis Type="Italic">ab initio </Emphasis> Quantum-Chemical Study of C<Subscript>6</Subscript>H<Subscript>5</Subscript>S(O)CH<Subscript>3</Subscript> and C<Subscript>6</Subscript>H<Subscript>5</Subscript>S(O)CF<Subscript>3</Subscript>

The potential functions of internal rotation around the C -S bond in the C₆H₅S(O)CH₃ and C₆H₅S(O)CF₃ molecules were obtained by ab initio MP2(full)/6-31+G* calculations. The stationary points were identified by solving the vibrational problems. The structures in which the plane of the C -S-C bonds is approximately perpendicular to the benzene ring plane correspond to the energy minimum. The barriers to rotation around the C -S bond, corrected for the zero-point vibration energy, are 21.29 [C₆H₅S(O)CH₃] and 28.98 [C₆H₅S(O)CF₃] kJ mol⁻¹. The bond angles (deg) are as follows: 95.7 (CSC), 107.1 (C SO), 106.3 (C SO) in C₆H₅S(O)CH₃; 93.5 (CSC), 108.2 (C SO), 105.2 (C SO) in C₆H₅S(O)CF₃. The bond lengths are as follows (Å): 1.520 (S=O), 1.804 (C -S), 1.810 (C -S) in C₆H₅S(O)CH₃; 1.507 (S=O), 1.799 (C -S), 1.870 (C -S) in C₆H₅S(O)CF₃. According to the results of NBO calculations, the formally double S=O bond consists of a strongly polarized covalent σ bond (S→O) and an almost ionic bond. An increase in the S=O bond multiplicity relative to a single bond is mainly due to hyperconjugation by the mechanism n(O)→σ*(C -S) and n(O)→σ*(C -S) and, to a lesser extent, by interaction of the oxygen lone electron pairs with the Rydberg orbitals of the S atoms, characterized by a large contribution of the d component.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 1, 2005, pp. 96–104.Original Russian Text Copyright © 2005 by Bzhezovskii, Il’chenko, Chura, Gorb, Yagupol’skii.     

Surface Fluorination of Carboxylated Nitrile Butadiene Rubber: An XPS Study

Because of their exceptional reactivity, fluorine and fluorinated gases are of primary importance for the modification of the surface properties of materials. This study is devoted to surface treatment of thin nitrile gloves, made of carboxylated nitrile butadiene rubber latex, using either direct fluorination (10% F₂gas diluted in N₂) or plasma-enhanced fluorination in radio-frequency cold plasmas using fluorinated gases (CF₄, CHF₃). Mechanisms of fluorination of these co-elastomers have been proposed on the basis of the assignment of the different components of the XPS spectra. Several mechanisms have been observed depending on the fluorination conditions. Although the modification of nitrile gloves is already effective for fluorination reactions at room temperature, an important activation is observed for experiments carried out at 90°C. When the treatments are carried out at room temperature, a gradual fluorination occurs: in the case of 10% diluted F₂ gas, monofluorinated C—F groups are the species most found at the surface and perfluoro groups CF _n are present in lower amount. An addition reaction takes place at the CH=CH double bonds of the polybutadiene entities, leading to CHF=CHF units. Whatever the fluorination method, thermal activation yields a more massive fluorination of the surface that finally leads to perfluorinated CF₂ groups and terminal —CF₃ groups.     

Structure Development in Simple Cross-Linked Organopolysiloxanes

13C CP and CPPI MAS NMR have been carried out on thermally cured samples of polymethylvinylsiloxane and polydimethylsiloxane. By varying the CP contact time, the and vinyl carbons and the methyl carbon of the CH3–(SiO<)–CH=CH2 species could be identified. A further methyl carbon was detected which was less mobile and which we assign to methyl groups attached to silicon species on which the vinyl group has reacted to form a cross-link. Resonance from – CH2– carbons was observed in the 30–40 ppm range, and these species arise from methyl-vinyl cross-linking to give CH3–(SiO<)– H2– H2–(SiO<)–CH=CH2. Higher temperature curing promotes vinyl-vinyl cross-linking to give CH3–(SiO<)–CH2– H–CH2–(SiO<)–CH3 links between chains. Evidence for this comes from the insensitivity of the carbon resonance under CPPI, indicating that it is in a – CH= rather than a =CH2 environment. There was also evidence of –CH2– carbons in the polydimethylsiloxane material, suggesting that thermally activated, methyl-methyl cross-linking can occur to give CH3–(SiO<)– H2– H2(SiO<)–CH3 links between chains.     

17O NMR Investigation of Chemical Homogeneity in Hybrid Systems

¹⁷O NMR experiments using enriched water were performed to followthe hydrolysis-condensation process of dimethyldiethoxysilanetetraethoxysilane and a 1/1 mixture of dimethyldiethoxysilane andtetraethoxysilane (H₂O/OEt = 0.5; pH = 2). The spectrarecorded over several hours time period were simulated to followquantitatively the variations of residual water, hydroxyl groups(Si–¹⁷ H) and oxo bridges (Si–¹⁷ –Si). Presence of a resonance signal due oxo bridges between di- andtetrafunctional Si units clearly demonstrates that co-condensationreactions occur to a large extent between the two alkoxides, and that thesebonds are stable during the aging period.     

Volumetric Properties of Binary Mixtures of Acetonitrile and Chloroalkanes at 25°C and Atmospheric Pressure

Excess molar volumes for binary mixtures of acetonitrile + dichloromethane, acetonitrile + trichloromethane, and acetonitrile + tetracloromethane at 25°C have been used to calculate partial molar volumes , excess partial molar volumes , and apparent molar volumes of each component as a function of composition. The V _m ^Evalues are negative over the entire composition range for the systems studied. The applicability of the Prigogine–Flory–Patterson theory was explored. The agreement between theoretical and experimental results is satisfactory for the systems with dichloromethane and tetrachloromethane. For the unsymmetrical behavior of the system with trichloromethane, however, the agreement is poor.     

Cluster Models of Co2+ at the Cation Sites of Zeolite ZSM-5

The local structure of Co₂₊ at the -, , and -cation sites of zeolite ZSM-5 was calculated in terms of density functional theory using the cluster approach. The local geometry of the oxygen environment of Co₂₊ is characterized; it is found that the ion stabilization energy increases in the series .     

Intramolecular Nonbonded Interactions Between Oxygen and Group VIA Elements: An Ab Initio Molecular Orbital and Density Functional Theory Investigation of the Structures of HX—CH2—COOH (X=S,Se, and Te)

Ab initio molecular orbital and density functional methods have been used to study the potential energy surfaces of the substituted acetic acids HX—CH₂—COOH, where X is one of the Group VIA Chalcophiles S, Se, or Te. The various conformers adopted by these compounds provide information regarding the energetic importance of nonbonded and hydrogen bonding interactions involving oxygen atoms with different hybridizations. Density functional and ab initio molecular orbital methods yield similar structural and energetic trends for these compounds. Calculations show that the structure of the lowest-energy conformer of each of these acids has the X—C—C—O backbone substantially twisted from planarity, similar to that previously observed for the corresponding aldehydes, HX—CH₂—CHO. In the twisted acid structures the shortest distance is within about 0.1 Å of the sum of the X and O van der Waals radii, which reduces overcrowding of the lone pairs of electrons on these atoms. In conformers where the heavy atom backbone is planar, one of the distances is significantly shorter than the sum of the van der Waals radii, and the total molecular energy of these conformers is higher than that of the twisted forms. The variation of X—H vibrational frequencies among conformers reflects the extent of X—H hydrogen bonding, and indicates that formation of this hydrogen bond is not the dominant factor in determining the lowest-energy conformation. When X is oxygen (HO—CH₂—COOH), the lowest-energy conformer is also nonplanar, whereas for the corresponding aldehyde, HO—CH₂—CHO, the lowest-energy conformer is a planar structure with C_S symmetry. The conformational preferences of these simple species provide reference points for inter- and intramolecular interactions in more complex systems of biological interest.     

Theoretical Investigation of the C2H2B2 Potential Energy Surface

Fifteen unique energy minima and thirteen transition states on the C ₂H₂B₂ potential surface have been located and optimized at the MP2 level of theory with the 6-311G(d,p) basis set. The planar four-membered ring isomer , 1, an analog of cyclobutadiene, is a transition state lying 37 kcal/mol above the nonplanar four-membered ring , 3. The planar , 10, is the second most stable species found, lying 72.2 kcal/mol below 3. The nonplanar, butterfly-shaped ring, 4, is a local minimum 33.7 kcal/mol more stable than 3. A four-membered ring isomer with alternating boron–carbon locations, , 5, lies 67.0 kcal/mol below 3 and 33.3 kcal/mol below 4. The ring of 5 is planar with one hydrogen above and one below the plane (C _2h symmetry). The borylene-substituted boracyclopropene, , 8, is a planar local minimum lying 36.0 kcal/mol above 5. The most stable C₂H₂B₂ isomer found was the planar, four-membered ring system 22 (D _2h symmetry) composed of two BCC three-membered rings fused across the C-C bond. Structure 22 lies 22.2 kcal/mole below 10, 105.4 kcal/mol below 3, 71.7 kcal/mol below 4, and 38.2 kcal/mol below 5. Isomer 22 is the structural analog of the trialene form of C₄H₂. The most stable linear isomer, HB BH, 26, was surprisingly 50.5 kcal/mol less stable than 22. The stabilities of the two most stable cyclic isomers 10 and 22 may be explained by aromaticity.     

Structural Investigation of the First Stages of Pyrolysis of Si-C-O Preceramic Polymers Containing Si–H Bonds

The polymer-to-glass transformation in the Si-C-O system usually involves cross-linking reactions at the C sites, which transform for example Si– H3 sites into (Si)4 sites, leading to the formation of a silicon oxycarbide network. Identification of the various C sites that form during pyrolysis under inert atmosphere is rather difficult from 13C MAS-NMR spectra, due to strong overlap of resonance lines, which prevents an accurate determination of the chemical shift values. This paper reports on the use of a spectral editing technique called Inversion Recovery Cross Polarization (IRCP), which, when combined with Cross Polarization (CP) technique, allows us to identify and quantify the formation of Si- H2-Si bridges during the early stages of the pyrolytic transformation of a polysiloxane containing Si–CH3 and Si–H groups. Several Si-C-O systems characterized by the same initial number of Si–CH3 bonds but with increasing number of Si–H bonds, have been investigated by MAS-NMR as well as thermogravimetric analysis coupled with mass spectrometry (TG/MS). The Si—H bonds play clearly an active role in the insertion of C atoms within the silica network.     

Preparation of Lithiated Co- and Ni-Oxide Powders and Thin Films by Wet Chemistry Processing

Layered lithiated Co- and Ni-oxide powders and thin films with rhombohedral (R m) structure were prepared by a peroxo wet chemistry route from Li(I), Co(II) and Ni(II) acetate precursors and the addition of H2O2. XRD analysis revealed that xerogel films and powders possessed a typical layered structure. Layered (R m) Li_0.99Co_1.01O₂ powder and Li_0.97Co_1.03O₂ films were formed around 500°C, while Li_0.93Ni_1.07O₂ powder and Li_0.94Ni_1.06O₂ oxide films were prepared around 550°C. The stoichiometry of the oxide films and powders was dependent on the heat-treatment temperature. The structure of sols, gels, xerogels and thin films was established from XRD spectra and from the FT-IR spectra, confirming their layered structure.     

Molecular Structure and Conformation of p-Bis(trimethylsilyl)benzene: A Study by Gas-Phase Electron Diffraction and Theoretical Calculations

The molecular structure and conformation of p-bis(trimethylsilyl)benzene have been investigated by gas-phase electron diffraction, ab initio MO calculations at the HF/6-31G*, MP2(f.c.)/6-31G*, and B3LYP/6-31G* levels, and MM3 molecular mechanics calculations. The calculations indicate the syn- and anti-coplanar conformations, with two bonds in the plane of the benzene ring, to be energy minima. The perpendicular conformations, with two bonds in a plane orthogonal to the ring plane, are transition states. The two coplanar conformers have nearly the same energy with a low interconversion barrier, 0.3–0.5 kJ mol^–1. The calculated lengths of the and bonds differ by only a few thousandths of an angstrom, in agreement with electron diffraction results from molecules containing either or bonds. The geometrical distortion of the benzene ring in p-bis(trimethylsilyl)-benzene may be described by superimposing independent distortions from each of the two SiMe₃ groups. The electron diffraction intensities from a previous study (Rozsondai, B.; Zelei, B.; Hargittai, I. J. Mol. Struct. 1982, 95, 187) have been reanalyzed, imposing constraints from the theoretical calculations, and using a model based on a 1:1 mixture of the two coplanar conformers. The effective torsion angles of the SiMe₃ groups may indicate nearly free rotation. Important geometrical parameters from the present electron diffraction analysis are , and . While the mean bond lengths are virtually the same from the previous and present analyses, the new ipso angle is in better agreement with the MO calculations [HF, 116.9° MP2(f.c.), 117.1° B3LYP, 116.9°].     

On the Pressure and Electric Field Dependencies of the Relative Permittivity of Liquids

The dependencies of the relative permittivity of over 50 liquids on the pressure P, as , and of some 40 liquids on the (square of the) electric field E at ambient conditions, as were obtained from literature data. The function was fitted to a simple expression in and the compressibility, _T. These data were used to obtain the limiting slope for the partial molar volumes and the electrostriction of electrolytes in various solvents.     

Ionic Mobility, Structure, Phase Transition, and Conductivity in (NH4)3Sb4F15

Fluoride and ammonium ion dynamics in (NH₄)₃Sb₄F₁₅ was studied by ¹H and ¹⁹F NMR spectroscopy in the range 180-440 K. Types of ionic motion were determined, and their activation energies were estimated. The crystal structure of a single crystal of (NH₄)₃Sb₄F₁₅ (space group ) was solved. In the range K, a reversible phase transition has been found. Based on the experimental values of conductivity of (NH₄)₃Sb₄F₁₅ ( S/cm at T = 440 K), this antimony(III) fluoride is classified as a superionic conductor.     

Mechanism of the Reaction of Xenon Tetraoxide with Hydrogen: A Photochemical Reaction

The dependence of the rate of a photochemical reaction of XeO₄with H₂on the concentrations of H₂and the diluent gases He and CO₂is studied at room temperature. The results are compared with the data for the dark reaction. A mechanism with the elementary energetic branched-chain reaction OH (v) + XeO₄OH + O + XeO₃is proposed to explain the results of the study.     

Excess molar volumes of 2-methylethylbenzene with benzene,methylbenzene or ethylbenzene at various temperatures

Excess molar volumes of benzene or methylbenzene + 2-methylethylbenzene at 25, 35 and 45°C and of ethylbenzene + 2-methylethylbenzene at 25°C have been determined from density measurements using a vibrating tube densimeter. Experimental V _m ^E values have been compared with calculated values based on the Flory theory.List of Symbols p _i characteristic pressure of pure component - reduced temperature of pure component - V ^E excess molar volume - V _i ^* characteristic volume of pure component - reduced volume of mixture - reduced volume of pure component i - X ₁₂ interaction parameter in Flory's theory - site fraction of component 2 - segment fraction of component 2     

Geometric and computational aspects of polymer reconfiguration

We examine a few computational geometric problems concerning the structures of polymers. We use a standard model of a polymer, a polygonal chain (path of line segments) in three dimensions. The chain can be reconfigured in any manner as long as the edge lengths and the angles between consecutive edges remain fixed, and no two edges cross during the motion. We discuss preliminary results on the following problems.Given a chain, select some interior edge , defining two subchains which are adjacent to . We keep the two subchains individually rigid and rotate one around while leaving the other fixed in space, while maintaining the vertex-angles at . We call this motion an edge spin at . An O(n ²) algorithm for this problem is given as well as an (nlogn) lower bound on the time complexity.In determining whether a chain can be reconfigured from one conformation to another, it is useful to consider reconfiguring through some canonical conformation. In our three-dimensional case, the most obvious choice is to flatten a chain into the plane. However, we demonstrate that determining if a given chain can be reconfigured into the plane without self-intersecting is NP-hard, even if the restriction that it must lie monotonically is added. We then provide an O(n) algorithm to decide if a chain has a non-crossing convex coil conformation (where all angles turn in the same direction), although we cannot yet decide if a sequence of motions to reconfigure a chain into a convex coil conformation exists.     

On the cycle index of point groups

In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers of sites of D lying on the symmetry elements for G.     

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).