Densities and Volumetric Properties of Binary Mixtures of Formamide with 1-Butanol, 2-Butanol, 1,3-Butanediol and 1,4-Butanediol at Temperatures between 293.15 and 318.15 K

The densities of binary mixtures of formamide (FA) with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, including those of the pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume, V _m ^E, partial molar volumes, and , at infinite dilution, and excess partial molar volumes, and , at infinite dilution were calculated. The variation of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interactions in these mixtures. The partial molar expansivities, and , at infinite dilution and excess partial molar expansivities, and , at infinite dilution were also calculated. The V _m ^E values were found to be positive for all the mixtures at each temperature studied, except for FA + 1-butanol which exhibits a sigmoid trend wherein V _m ^E values change sign from positive to negative as the concentration of FA in the mixture is increased. The V _m ^E values for these mixtures follow the order: 1-butanol < 2-butanol < 1,3-butanediol < 1,4-butanediol. It is observed that the V _m ^E values depend upon the number and position of hydroxyl groups in these alkanol molecules.     

The First Structurally Characterized Mn(III) Substituted Sandwich-type Polyoxotungstates

The new polyoxotungstates H₂O (1), · 28H₂O (2) and H₂O (3) were synthesized in aqueous solution and characterized by IR and Raman spectroscopy, energy dispersive X-ray fluorescence and single-crystal X-ray analysis. The anions in 1 and 2 are the first structurally characterized sandwich-type polyoxoanions which contain trivalent manganese atoms. The manganese atoms are coordinated by four oxygen atoms of two Keggin fragments and one water molecule, forming a square pyramid. The manganese(II) containing anions in 3 are linked via Mn–O–W-bonds, forming a two-dimensional network.Dedicated to Prof. M.T. Pope on the occasion of his retirement.     

Mechanism of the catalyzed by cysteine electroreduction of the insoluble in water cobalt(II) salt as a component of carbon paste electrode

The mechanism of the Co(II) catalytic electroreduction of water insoluble CoR₂ salt in the presence of cysteine was developed. CoR₂ = cobalt(II) cyclohexylbutyrate is the component of a carbon paste electrode. Electrode surface consecutive reactions are: (a) fast (equilibrium) reaction of the complex formation, (b) rate-determining reversible reaction of the promoting process of CoR(Ac⁺) complex formation, (c) rate-determining irreversible reaction of the electroactive complex formation with ligand-induced adsorption, and (d) fast irreversible reaction of the electroreduction. Reactions (a,b) connected with CoR₂ dissolution and reactions (c,d) connected with CoR₂ electroreduction are catalyzed by . Regeneration of (reactions “b,d”) and accumulation of atomic Co(0) (reaction “d”) take place. Experimental data [Sugawara et al., Bioelectrochem Bioenergetics 26:469, 1991]: i _a vs E (i _a is anodic peak, E is cathodic accumulation potential), i _a vs , and i _a vs pH have been quantitatively explained.     

Effect of Ammonium Salts on the Volumetric and Viscometric Behavior of D(+)-Glucose,D(−)-Fructose and Sucrose in Aqueous Solutions at 25°C

Apparent molar volumes, V _φ, and viscosity, η, of D(+)-glucose, D(−)-fructose and sucrose in water and in 0.02, 0.05, 0.5, 1.0 and 2.0 mol·kg⁻¹ aqueous solutions of ammonium bromide, tetraethylammonium bromide and tetra-n-butylammonium bromide have been determined at 25 °C from density and efflux time measurements by using a vibrating-tube digital densimeter and a capillary viscometer, respectively. Partial molar volumes, , at infinite dilution that were extrapolated from the V _φ data were used to obtain the corresponding transfer volumes, , for saccharides from water to different aqueous solutions of co-solutes. The Jones-Dole equation viscosity B-coefficients were obtained from the viscosity data. Positive values of were obtained for the saccharides in the presence of ammonium bromide, whereas both positive and negative values were obtained in the presence of tetraethylammonium and tetra-n-butylammonium bromides. The negative values at very low concentrations have small magnitudes. Volumetric interaction coefficients have been calculated by using the McMillan-Mayer theory and Gibbs energies of activation of viscous flow have been calculated by using Feakin’s transition-state theory equation. The parameters obtained from the volumetric and viscometric studies were used to understand various mixing effects due to the interactions between saccharides and ammonium salts in aqueous solutions.     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

On the charge storage mechanism at RuO<Subscript>2</Subscript>/0.5 M H<Subscript>2</Subscript>SO<Subscript>4</Subscript> interface

Comparative study of capacitative properties of RuO₂/0.5 M H₂SO₄ and Ru/0.5 M H₂SO₄ interfaces has been performed with a view to find out the nature of electrochemical processes involved in the charge storage mechanism of ruthenium (IV) oxide. The methods of cyclic voltammetry and scanning electron microscopy (SEM) were employed for the investigation of electrochemical behavior and surface morphology of RuO₂ electrodes. It has been suggested that supercapacitor behavior of RuO₂ phase in the potential E range between 0.4 and 1.4 V vs reference hydrogen electrode (RHE) should be attributed to double-layer-type capacitance, related to non-faradaic highly reversible process of ionic pair formation and annihilation at RuO₂/electrolyte interface as described by following summary equation:

Germyl mesolytic dissociations in the allylgermane and penta- 2,4-dienylgermane radical anions. A theoretical study

In two stable structures have a trigonal bipyramidal arrangement around Ge, with the extra electron in equatorial (tbp eq) or axial (tbp ax) position. In only tbp ax is found, while a second structure with a tetrahedral germyl group has the extra electron on the conjugated π system. C−Ge bond cleavage yields allyl/ pentadienyl radicals plus germide. Both dissociation reactions require 4–6 kcal mol⁻¹, less than the analogous C and Si systems (ca. 30 and 14 kcal mol⁻¹, respectively). Fragmentation is dramatically activated with respect to homolysis in the corresponding neutrals. The wavefunction is dominated by one single configuration at all distances, in contrast to homolytic cleavage, in which two configurations are important. C−Ge bond dissociation is at variance also with heterolysis, due to spin recoupling of one of the C−Ge bond electrons with the originally unpaired electron. Contribution to the Fernando Bernardi Memorial Issue.     

Binuclear cobalt(II/II) and cobalt(II/III) chelates with O<Subscript>2</Subscript>N<Subscript>2</Subscript> ligands: synthesis,structure and magnetic studies

Abstract  The title complexes and have been synthesized in excellent yields by reacting Co(OAc)₂·4H₂O with H₂L¹ and H₂L², respectively, in acetonitrile solution. Here, [L¹]²⁻ and [L²]²⁻ are the deprotonated forms of N,N-bis(2-hydroxybenzyl)-N′,N′-dimethylethylenediamine and N,N-bis(2-hydroxybenzyl)-2-picolylamine, respectively. The crystal structures of and were determined by x-ray crystallography. In , each cobalt atom has distorted trigonal bipyramid geometry, while in , each cobalt atom has distorted octahedral geometry. Variable temperature magnetic moment measurements show weak antiferromagnetic interaction in . The magnetic characterization for is in agreement with the presence of Co(II) and Co(III) centers. Graphical Abstract  The title complexes and have been synthesized in excellent yields by reacting Co(OAc)₂·4H₂O with dianionic N₂O₂ coordinating ligands. In complex 1, each cobalt atom has distorted trigonal bipyramid geometry, while in complex 2, each cobalt atom has distorted octahedral geometry. Variable temperature magnetic moment measurements show weak antiferromagnetic interaction in complex 1. The magnetic characterization for complex 2 is in agreement with the presence of Co(II) and Co(III) centers. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, , is studied. After deriving and investigating general formulas for μ arbitrary complex, a detailed discussion of , where m is a non-negative integer, is carried out. The results are applied to obtain several explicit expressions for the associated Legendre function of the second kind of integer degree and order, . In particular, we arrive at formulas which generalize to the case of (0 ≤ m ≤ n) the well-known Christoffel’s representation of the Legendre function of the second kind, Q _n (z). The derivatives and , all with m > n, are also evaluated.     

Effect of the mediator in feedback mode-based SECM interrogation of indium tin-oxide and boron-doped diamond electrodes

Indium tin-oxide (ITO) and polycrystalline boron-doped diamond (BDD) have been examined in detail using the scanning electrochemical microscopy technique in feedback mode. For the interrogation of electrodes made from these materials, the choice of mediator has been varied. Using ferrocene methanol (FcMeOH), and approach curve experiments have been performed, and for purposes of comparison, calculations of the apparent heterogeneous electron transfer rates (k _app) have been made using these data. In general, it would appear that values of k _app are affected mainly by the position of the mediator reversible potential relative to the relevant semiconductor band edge (associated with majority carriers). For both the ITO (n type) and BDD (p type) electrodes, charge transfer is impeded and values are very low when using FcMeOH and as mediators, and the use of results in the largest value of k _app. With ITO, the surface is chemically homogeneous and no variation is observed for any given mediator. Data is also presented where the potential of the ITO electrode is fixed using a ratio of the mediators and In stark contrast, the BDD electrode is quite the opposite and a range of k _app values are observed for all mediators depending on the position on the surface. Both electrode surfaces are very flat and very smooth, and hence, for BDD, variations in feedback current imply a variation in the electrochemical activity. A comparison of the feedback current where the substrate is biased and unbiased shows a surprising degree of proportionality.Dedicated to Alan, a good friend and colleague on his 60th birthday.     

Cluster Oxalate Complexes [W3(μ3-Q)(μ2-Q)3 (C2O4)3(H2O)3]2? (Q=S, Se): Mechanochemical Synthesis and Crystal Structure

Mechanochemical reaction of cluster coordination polymers (Q=S, Se) with solid leads to the cluster core excision with the formation of anionic complexes . Extraction of the reaction mixture with water followed by crystallization gives crystalline (main product) and (1) (minor product). In the case of the Se cluster, the complex could not be isolated, and the treatment of the aqueous extract with PPh₃ gave (2) in a low yield. Alternatively, it was obtained from and in high yield. Both 1 and 2 were characterized by X-ray structure analysis. Dedicated to Academician I. I. Moiseev on the occasion of his 75th birthday and in recognition of his outstanding contribution to cluster chemistry.     

Photoelectrode characteristics of an organic bilayer in water phase containing a redox molecule

We have recently reported that the organic bilayer of 3,4,9,10-perylenetetracarboxyl-bisbenzimidazole (PTCBI, n-type semiconductor) and 29H,31H-phthalocyanine (H₂Pc, p-type semiconductor), which is a part of a photovoltaic cell, acts as a photoanode in the water phase (Abe et al., ChemPhysChem 5:716, [2004]); in that case, the generation of the photocurrent involving an irreversible thiol oxidation at the H₂Pc/water interface took place to be coupled with hole conduction through the H₂Pc layer, based on the photophysical character of the bilayer. In the present work, the photoelectrode characteristics of the bilayer were investigated in the water phase containing a redox molecule , where the photo-induced oxidation and reduction for the couple were found to take place at the bilayer. The photoanodic current involving the oxidation efficiently occurred at the interface of H₂Pc/water, similar to the previous example. In the view of the voltammograms obtained, it was noted that there are pin-holes in the H₂Pc layer of the bilayer, leading to a cathodic reaction with at the PTCBI surface especially in the dark; that is, the band bending at the PTCBI/water interface can essentially be reduced by applying a negative potential [e.g., < ∼ 0 V (vs Ag/AgCl)] to the PTCBI, when the cathodic reaction may take place through the conduction band of the PTCBI. Moreover, under that applied potential condition of irradiation, the photogenerated electron carrier part can move to the PTCBI surface, thus enhancing the reduction of .     

Direct and exchange contributions to inner and outer radii in many-electron atoms

Within the Hartree-Fock framework, the spinless two-electron density function Γ (r ₁, r ₂) consists of direct Γ_di (r ₁, r ₂) and exchange Γ_ex (r ₁, r ₂) parts. Accordingly, the inner and outer radii in many-electron systems are rigorously separated into the direct and exchange contributions, i.e., and . It is generally shown that and , where is the usual average radius of an electron. Numerical examinations of the direct and exchange contributions for the 102 atoms from He to Lr in their ground states find that the electron exchange works to decrease and increase . However, the exchange parts are very small and the direct parts essentially govern the inner and outer radii.     

Electrocatalytic Reduction of O2 by a Cu(II)-Substituted Electron-Rich Wheel-Type Oxomolybdate Nanocluster

Catalysis of electron transfer by a Cu-substituted wheel-type oxomolybdate cluster–anion, , (1), is demonstrated. Data provided include aqueous-solution chemistry (stability) studies of 1 and , (2), derivatives of the “plenary” {Mo₁₅₄} anion, , (3). Combined use of cyclic voltammetry and UV–vis spectroscopy shows that, while both 1 and 2 appear to be stable in solution at pH 0.33 (0.5 M H₂SO₄), 1 is more stable than 2 at pH 3 (in 0.2 M Na₂SO₄). Cyclic voltammetric analysis in the presence of O₂ shows that 1 is an electrocatalyst for electron transfer to O₂. Bulk electrolysis of 1 in the presence of O₂ (ca. 1 mM) is used to assess catalyst stability under turnover conditions, and to demonstrate that the final product of electrocatalytic reduction is water, rather than H₂O₂. Finally, control experiments using 1, 2, and CuSO₄ (no oxomolybdate-cluster present), show that catalytic activity is due to specific interaction(s) between Cu ions and the Mo₁₄₂ type oxomolybdate structure of 1.     

Unified treatment of complete orthonormal sets for exponential type vector orbitals of particles with spin 1 in coordinate, momentum and four-dimensional spaces

The new formulas are obtained for complete orthonormal sets of exponential type vector orbitals of a particle with spin 1 in coordinate, momentum and four-dimensional spaces using the properties of spherical vectors and complete orthonormal scalar basis sets of -exponential type orbitals ( -ETO), -momentum space orbitals ( -MSO) and -hyperspherical harmonics ( -HSH) introduced by the author for particles with spin s = 0, where These vector orbitals are complete without the inclusion of the continuum and, therefore, their group of transformation is the four-dimensional rotation group of O(4). For overlap integrals over vector Slater orbitals with the same screening constant the analytical relations in coordinate space are also derived. It should be noted that the new idea presented in this study is the combination of spherical vectors with complete orthonormal scalar sets for radial parts of -orbitals.     

Relationship between current response and time in ion transport problem including diffusion and convection. 1. An analytical approach

   The mathematical models of the ion transport problem in a potential field are anayzed. Ion transport is regarded as the superposition of diffusion and convection. In the case of pure diffusion model the classical Gottrell’s result is studied for a constant as well as for the time dependent Dirichlet data at the electrode. Comparative analysis of the current response and the classical Gottrellian is given on the obtained explicit formulas. The approach is extended to find out the current response corresponding to the diffusion-convection model. The relationship between the current response and Gottrellian is obtained in explicit form. This relationship permits one to compare pure diffusion and diffusion-convection models, including asymptotic behaviour of current response and an influence of the convection coefficient. The theoretical result are illustrated by numerical examples.      

Interfacial behavior of sulforhodamine 101 at the polarized water/1,2-dichloroethane interface studied by spectroelectrochemical techniques

The transfer mechanism of an amphoteric rhodamine, sulforhodamine 101 (SR101), across the polarized water/1,2-dichloroethane (DCE) interface was investigated using cyclic voltammetry, differential voltfluorometry and potential-modulated fluorescence (PMF) spectroscopy. The voltammetric response for the ion transfer of SR101 monoanion from water to DCE was observed as the diffusion-controlled transfer process. An unusual voltammetric response was found at 0.15 V more negative than the formal transfer potential of SR101⁻ in the cyclic voltammogram and voltfluorogram. The frequency dependence of the PMF responses confirmed the presence of the adsorption processes at negative potentials. In addition, a further transient adsorption step was uncovered at The interfacial mechanism of SR101 is discussed by comparing the results obtained from each technique.     

On zeroth-order general Randić index of conjugated unicyclic graphs

Let G be a graph and d _v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as where α is an arbitrary real number. In this paper, we investigate the zeroth-order general Randić index of conjugated unicyclic graphs G (i.e., unicyclic graphs with a perfect matching) and sharp lower and upper bounds are obtained for depending on α in different intervals.     

Effect of charge on the standard partial molar volumes and heat capacities of organic electrolytes in methanol and water

Previously developed additivity schemes for nonelectrolytes have been used to estimate and for tetraalkyl and tetraphenyl methanes in methanol and water. Corrections have been applied to the thermodynamic values of these model compounds to account for a variation in size of the central atom, and these were used to ascertain the effect of charge on and of alkyl and phenyl quaternary ions having N, P and B as central atoms. Investigations of R₄NBr, (R=methyl to heptyl) salts show that the charge effect on and of R₄N⁺ ions is large and relatively independent of ion size suggesting that the solvent molecules penetrate the ions. The ability to estimate and of the quaternary ions in the bromide salt solutions has made it possible to make ionic assignments with some confidence; (Br^–) has been evaluated as 19.7±2 and 30.2±7 cm³-mol^–1 and (Br^–) as –83±7 and –68±30 J-K^–1-mol^–1 in methanol and water, respectively. The use of organic ions for making ionic assignments of and is critically examined and comparisons with other assignments are made. The scaled particle theory is employed to divide the heat capacities of electrolytes into cavity and interaction contributions.