Analytical formulae for chronoamperometry of a charge neutralisation process under conditions of linear migration and diffusion

The electrochemical reaction of the charge neutralisation of a binary electrolyte ion, at a planar electrode, is a rare example for which analytical formulae for potential step chronoamperometry can be obtained, under conditions of migration-diffusion transport in semi-infinite, one-dimensional space domain. This has been previously shown by Myland and Oldham [Electrochem. Commun. 1 (1999) 467], assuming equal diffusion coefficients. In the present work, a more general analytical solution is obtained, for the case of unequal diffusion coefficients. The effect of the diffusion coefficient ratio D_R/D_C, of the electroactive ion R and the counter-ion C, on the limiting chronoamperometric current, is examined. The effect increases with the growing ratio |z_R/z_C| of the electric charges of these ions, and becomes nonnegligible for |z_R| greater than or equal about 2, and for typical departures of D_R/D_C from unity. Among other things, the formulae obtained can be useful for testing digital simulation methods for the Nernst–Planck equations.     

Diffusion coefficients of ions through ion excange membrane in Donnan dialysis using ions of different valence

Donnan dialysis with an ion exchange membrane was investigated for ions of different valence. The effective diffusion coefficients (D_e) of various kinds of ions in the membrane were obtained by fitting of the equation derived from the Nernst–Planck equation to three or more sets of experimental data for Donnan dialysis. It became apparent that the value of D_e/D_s of monovalent ions (e.g., K⁺ or Na⁺ ions) at z_A=1 and z_B=2 (feed ions are monovalent ones and driving ions are bivalent ones) remained constant at ca. 1/210 and that of bivalent ions (e.g., Ca²⁺, Cu²⁺, or Mg²⁺ ions) remained constant at ca. 1/526 where D_s denotes the diffusion coefficient of ions at infinite dilution in water calculated from the Nernst–Einstein equation, and z_A and z_B represent the valences of the feed and driving ions, respectively. D_e/D_s of monovalent ions (e.g., H⁺, K⁺, or Na⁺ ions) at z_A=2 and z_B=1 (feed ions are bivalent ones and driving ions are monovalent ones) was constant at ca. 1/23.3 and that of bivalent ions remained constant at ca. 1/58.4. It was proved that D_e/D using D_e at z_A=1 and z_B=2 was constant at 1/3.0 and that at z_A=2 and z_B=1 remained constant at 3.0 where D represents the diffusion coefficient of ions in the membrane at z_A=z_B (the valences of both feed and driving ions are equal). Therefore, it was found that a large flux of ions could be obtained using the monovalent driving ions in Donnan dialysis. On the other hand, the small flux can be obtained using bi- or higher-valent driving ions.     

Variation of interatomic distances in oxides

The average interatomic distances D in oxygen polyhedra MO _n of isostructural oxides were proposed to be estimated using the equation D = Kɛ(R _M + R _O) or D = Ax ² + Bx + C, where x = ɛ(R _M + R _O), ɛ is the ionicity of the M-O bond, R _M is the ionic radius of the cation M with account for the coordination in the polyhedron, and R _O is the ionic radius of oxygen. Calculations were made for MO oxides having the rock-salt structure; Ln₂O₃ oxides, where Ln = Ce-Yb; and the MO₂ oxides having the rutile and fluorite structures.     

Hyperfine structure of the resonance lines of53Cr and lifetimes of some excited states of the Cr I spectrum

The hyperfine structure of the⁵³Cr resonance linesa ⁷ S ₃ ?z ⁷ P _2,3,4 has been investigated by means of laser saturation spectroscopy. By comparison of the experimental signal curves with theoretically computed spectra the hitherto unknown sign of the magnetic hyperfine coupling constant in thea ⁷ S ₃ ground state of⁵³Cr could be determined unambigiously to be negative. Further the signs of the hfs coupling constants in thez ⁷ P states — so far only evaluated by theoretical reasoning — could be confirmed. Additionally the lifetimes of the statesz ⁷ P,z ⁵ P,f ⁷ D,z ⁵ F,e ⁷ D ₅ andy ⁵ P ₃ in the Cr I spectrum have been determined from the fluorescence decay after pulsed laser excitation.     

Electron impact ionization and dissociation of neutral and charged fullerenes

Three different types of electron impact ionization experiments have been performed, involving neutral and charged C₆₀ and C₇₀. 1) We have determined absolute partial ionization cross sections for formation of parent ions C ₆₀ ^z+ and C ₇₀ ^z+ in charge states up to z = 4, and of singly and multiply charged fragments of size n ≥ 44 and n ≥ 50 from C₆₀ and C₇₀ neutral precursors, respectively. 2) Previous appearance energy measurements of C₇₀ have been improved and extended to z = 5; ionization energies are found to depend linearly on the charge state of the precursor, in agreement with theoretical predictions. 3) A beam of mass selected C ₆₀ ²⁺ has been crossed with an intense electron beam; the induced reactions (fragmentation, post- ionization, and dissociative post-ionization) have been analyzed.     

Copolymerization of acrylic acid to nylon-6 by trapped radicals—I. Vapour phase grafting

Film of nylon-6 has been γ-irradiated in vacuo to various doses D. Grafting has been effected by subsequent exposure in vacuo to vapour at 50° of composition 9.1 wt% acrylic acid and 90.9 wt% water. Determinations have been made of total vapour uptake as well as the individual swellings due to monomer and water. For D ? ca. 2 Mrad, the initial rate of grafting R_g increased with D in accord with R_g ∝ D^β with β = 0.45 ± 0.05, thus suggesting bimolecular chain termination. However, for D ? ca. 2 Mrad, there is no further increase in R_g. This is attributed in part to the fact that the radical yield is proportional to dose only for D ? ca. 2.5 Mrad. Diffusion controlled grafting has been predicted elsewhere to be characterized by β = 0.67. Grafting proceeds from the surface and the initial stages are concluded to be essentially free from diffusion control, since (a) β ≠ 0.67, (b) the rate of uptake of monomer vapour >R_g and (c) a large change in film thickness yields only a very small change in R_g.     

Neutron diffraction study of Na2UO2(C2O4)2 · 5D2O

A sample of Na₂UO₂(C₂O₄)₂ · 5D₂O (I) was studied by powder neutron diffraction. The compound crystallizes in the triclinic system, space group P1, unit cell parameters: a = 6.934(1) ?, b = 7.566(1) ?, c = 15.409(2) ?, ?? = 94.720(6)°, ?? = 96.281(6)°, ?? = 111.765(5)°, Z = 2, R _F = 5.35, R _I = 6.73 and ??² = 2.89. The hydrogen bonds and non-valence contacts involved in the formation and binding of the {Na₂[UO₂(C₂O₄)₂(D₂O)](D₂O)₄} layers in I were analyzed using the Voronoi-Dirichlet polyhedra.     

Electronic shell structure in multiply charged silver clusters

Silver clusters are generated by standard laser vaporization technique and ionized via multiphoton ionization. Time-of-flight mass spectrometry reveals singly, doubly and triply charged clusters, Ag _n ^z+ (z=1,2,3). The spectra show, for all charge states, intensity variations, indicating enhanced stabilities for cluster sizes with closed electronic configurations in accord with the spherical jellium model.     

SOLUTION STUDY AND CRYSTAL STRUCTURE OF A PENTACOORDINATE ZINC(II) COMPLEX WITH N,N″-bis-(2-HYDROXYBENZYL)-DIETHYLENETRIAMINE

Abstract

The stability constants of Zn(II) complexes with N,N″-bis-(2-hydroxybenzyl)-diethylenetri-amine(H₂L) were determined by potentiometric pH titration at 25°C and at 0.1 M KNO₃ ionic strength. A neutral complex ZnL was synthesized. In addition to IR, and ¹H NMR spectra, its structure was established by single crystal X-ray diffraction. The crystal is orthorhombic, of space group Pbca, with cell constants a = 17.865(4), b = 20.079(4), c = 9.598(2)Å, z = 8 and D_c = 1.461 g°Cm^?3. The structure was solved and refined to R = 0.049 (R_w = 0.054). The coordination geometry around the zinc ion is trigonal-bipyramidal with a large distortion, exhibiting two nonequivalent phenolates.     

Spin polarization in the lowest triplet state of chlorophyll

Chlorophyll-b in glassy solution has a spin-polarized lowest triplet state at and above 77 K. The magnitude of the effect is different for MTHF and ethanol as solvents, in contrast to what is found for the porphin free base. Chlorophyll-a does not exhibit spin-polarization under identical conditions as for chlorophyll-b. Zero-field parameters are found to be:chlorophyll-a (MTHF) D = (281 ± 6) × 10^?4 cm^?1; E = (39 ± 3) × 10^?4 cm^?1;chlorophyll-b (MTHF) D = (289 ± 4) × 10^?4 cm^?1; E = (49 ± 3) × 10^?4 cm^?1,From ESR signal kinetics it follows that for chlorophyll-b, population and depopulation mainly involve the spin level y?, describing a spin moving in a plane perpendicular to the molecular plane:P_y ? P_x ? P_z; k_x = 240 ± 40 s^?1; k_y = 600 ± 120 s^?1; k_z ? 75 s^?1,where P_i and k_i denote populating and decay rates. Thus, the kinetic scheme for the chlorophyll triplet is different from that of porphyrins with heavier metal ions, but very similar to that of the porphin free base. The spin-lattice relaxation time is found to be anisotropic and shorter than the decay rates of individual spin levels. Nevertheless, spin polarization can be observed, essentially because the ESR signal amplitude depends on population differences.     

Crystal structure and properties of the [Cu(C11H10N4)Br2] compound. Stereochemistry of [Cu(planar tridentate ligand)(unidentate ligand)2] complexes

The crystal structure of the dibromo(pyridine-2-aldehyde 2′-pyridylhydrazone) copper(II) is reported. The compound crystallizes in space group P2₁/_n, with a = 12.86(2), b = 11.944(5), c = 8.770(7) Å, β = 97.17(6)°, U = 1336(3) ų, Z = 4, D_m = 2.06(1), D_x= 2.10 g cm⁻³, μ(Mo-K_α) = 78.92 mm⁻¹, F(000) = 812, T = 293 K. Final R is 0.047 (R_w = 0.049) for 854 observed reflections. The structure consists of discrete molecules in which the copper(II) ion is pentacoordinate with a distorted square pyramidal geometry. The spectroscopic data are in good agreement with the structural results. The stereochemistry of several pentacoordinate complexes of type [Cu(planar tridentate ligand) (unidentate ligand)₂] is examined and the distortions of the coordination polyhedra are calculated.     

Hindered diffusion of synthetic polyelectrolytes in charged microporous membranes

To examine electrostatic effects on the diffusion of macromolecules in membranes, diffusivities of narrow molecular-size fractions of the polyelectrolytes ficoll sulfate and dextran sulfate were measured in polycarbonate track-etch membranes. Radius, number density, and surface charge density of membrane pores were determined from a combination of hydraulic permeability, glucose diffusion, and streaming potential measurements. Molecular charge and Stokes—Einstein radius for each macromolecule fraction were determined from free-solution electrophoretic mobility and diffusivity in a large pore radius membrane, D∞, respectively. As ionic strength was increased from 0.005 to 0.1 M, D∞ for ficoll sulfate remained constant while D∞ for dextran sulfate increased slightly (15-18%). Macromolecule diffusivities in small pore membranes, D, were much more sensitive to ionic strength. For membranes where the ratio of Stokes—Einstein radius to pore radius ranged from 0.08 to 0.29, D/D∞ for ficoll sulfate and dextran sulfate increased by factors ranging from 2.5 to 14 for the same increase in ionic strength. Recent theoretical results for electrostatic double layer interactions in hindered diffusion are in good quantitative agreement with these findings.     

The crystal structure of the 42-Å subcell of a layer structure with approximate composition Ba4Nb2S9

Platy crystals from the products of a mixture 4 Bas : 2 Nb : 5 S reacted at 1000°C have cell constants a = 13.754(3) Å, c = 83.73(2) Å, $\text{R}\text{3}\text{m}$. The reciprocal lattice had a pronounced subcell with dimensions a = 6.877(1) Å, c = 41.84(1) Å, same space group. Three dimensional X-ray diffraction data were collected using monochromatized Mo Kα radiation and of 5051 measured intensities 1892 were considered observed. From the set of observed intensities 611 reflections having all even indices were used to refine the crystal structure of the 42 × 7-Å subcell. The final R = 0.036 and ωR = 0.052 for the 611 observed amplitudes and R = 0.046, ωR = 0.052 for all 711 amplitudes of the subcell. The structure is based on the stacking of hexagonal BaS₃ layers with the sequence DABABDBCBCDCACAD. The D layer denotes a disordered level and occurs at $\text{z = 0,}\text{1}\text{3}$ and $\text{2}\text{3}$. The different letters for the ordered layers are based on the Ba positions in that layer. The Nb ions occupy octahedral interstices and form a unit of three face sharing octahedra parallel to c. The column is terminated above and below by disordered levels. The NbNb distances are 3.22 Å, causing displacement of Nb from the centers of the two outside octahedra. One Ba is in the center of a triangular orthobicupola formed by 12 S atoms. The other Ba is in the center of a hexagon of 6 S with 3 additional S above this layer forming $\text{1}\text{2}$ of a cuboctahedron. The lower half consists of a disordered layer of atoms. The NbS distances are 2.279, 2.433, and 2.683 Å; BaS distances vary between 3.1 and 3.5 Å. The subcell content based on the ordered structure only is Ba₁₂Nb₉S₃₆. The placement of disordered Ba and S at $\text{z = 0,}\text{1}\text{3}$, and $\text{2}\text{3}$ levels of the subcell leads to the unlikely composition Ba_16.5Nb₉S₄₂. The ordered structure most likely has a composition Ba₄Nb₂S₉, z = 36, so that the subcell composition should be Ba₁₈Nb₉S_40.5. The completely ordered structure has not been solved.     

Neutron diffraction study of uranyl oxalate [UO2(C2O4)(D2O)] · 2D2O

A powdered sample of uranyl oxalate [UO₂(C₂O₄)(D₂O)] · 2D₂O (compound I) is studied using neutron diffraction. The crystals are monoclinic, space group P2₁/c, with a = 5.608(1) Å, b = 17.016(3) Å, c = 9.410(2) Å, β = 98.9369(2)°, Z = 4, R _f = 0.042, R _I = 0.054, x ² = 1.5. The main structural units of the crystals are [UO₂(C₂O₄)(D₂O)] chains. These chains, which belong to the AK⁰²M¹ (A = UO ₂ ²⁺ ) crystal-chemical group of the uranyl complexes, lie parallel to [101]. The water molecules in the crystals of I are hydrogen-bonded into zigzag chains running along [100]. Since each third oxygen atom of the chain formed of water molecules is coordinated to the uranium atom, the uranyl oxalate chains are linked into {[UO₂(C₂O₄)(D₂O)] · 2D₂O} layers that lie normal to [010]. The layers are linked into the framework through interlayer hydrogen bonds (D₂O)O-D···O (oxalate).     

J and term dependences in the isotope shift of Eu I

High-resolution laser atomic beam spectroscopy has been applied to studyJ and term dependences in the isotope shift of the levels 4f ⁷5d6s a ¹⁰ D _J ,a ⁸ D _J of Eu I. A parametric analysis of the isotope shift has been performed. TheJ dependence is interpreted through two term-dependent parametersz _5d , and the term dependence through one parameterΔT:z _5d (a ¹⁰ D)=44.1 (2.6) MHz,z _5d (a ⁸ D)=55.9 (2.3) MHz,ΔT=408.5 (3.2) MHz. Ab initio Hartree-Fock and Dirac-Fock calculations have been made to interpret these parameters. Within the accuracy of the calculations the parameters can be attributed to field shift effects.     

Determination of binding constants of multiple charged cyclodextrin complexes by ACE using uncorrected and ionic strength corrected actual mobilities of the species involved

In this study, the apparent binding constants and limiting mobilities of the multiply charged complexes of the Δ− and Λ−enantiomers of Ru(II)- and Fe(II)-polypyridyl associates ([Ru(2,2′-bipyridine)₃]²⁺, [Ru(1,10-phenanthroline)₃]²⁺, and [Fe(1,10-phenanthroline)₃]²⁺) with single-isomer 2,3-diacetylated-6-sulfated-cyclodextrins (CDs) (12Ac-6S-α-CD, 14Ac-7S-β-CD, and 16Ac-8S-γ-CD) were determined by ACE using uncorrected and ionic strength corrected actual mobilities of the species involved. Two limiting models were tested for the ionic strength correction of the actual mobilities based on an empirical relation for the ionic strength correction of multivalent ionic species. In model 1, the nominal values of the charge numbers (z_S,nom) and analytical concentrations (c_S,nom) of the above CD selectors in the BGEs were applied for calculation of the BGE ionic strength, as usual. In model 2, the CD selectors were considered as singly charged species (z_S = −1) with |z_S,nom|-times higher concentrations in the BGE than their analytical concentrations (c_S = |z_S,nom| × c_S,nom) in the calculation of the BGE ionic strength. In all three cases–with uncorrected actual mobilities as well as with actual mobilities corrected according to the two limiting models–the measured effective mobilities of the above enantiomers fit well the theoretical curves of their mobility dependences on the CD selectors concentrations in the BGE, with high average coefficients of determination (R² = 0.9890–0.9995). Nevertheless, the best physico-chemically meaningful values of the apparent binding constants and the limiting mobilities of the enantiomer-CDs complexes with low RSDs were obtained using the actual mobilities of the species involved corrected according to model 2.     

Spin-orbit perturbation of the anion states by a heavy cation in NaNO2:Ag+

Optical and ODMR studies of NaNO₂: Ag⁺ crystals at T < 4.2 K have shown very selective spin-orbit perturbations on the properties of the nitrite triplet state T₁, by the heavy cation dopant. The perturbed T₁ — S₀ transition shows mainly z-axis polarization associated with the τ_y spin state (z- and y-axes in-plane with the z-axis bisecting the ONO angle). The fine structure splitting constants for the perturbed T₁ state are D = -3Y/2 = ± 15.508 GHz and E = (Z - X)/2 = 3 .643 GHz.     

Synthesis of unusual mixed ligand tellurium(IV) dithiocarbamates with perchlorate. Crystal and molecular structure of perchloratotris(diethyldithiocarbamato)tellurium(IV)

Synthetic and structural aspects of perchlorato complexes of tellurium(IV) with different dithiocarbamates (dtc) [(R₁R₂NCS₂) where R₁ = R₂ = methyl, ethyl, n-propyl, i-propyl; R₁R₂ = (CH₂)₅(piperidine), C₂H₄OC₂H₄ (morpholine)] are reported. The crystal structure of TeL₃ClO₄ (where L = diethyl dtc) has been determined. The crystals of the complex are monoclinic, space group P2₁/n, a = 11.379(3), b = 17.745(7), c = 14.016(8) Å, γ = 103.30(2)°, V = 2754.2 ų, F(000) = 1352, D_X = 1.61 mg M−3. The final R and R_w values are 0.047 and 0.058, respectively for 5224 unique reflections. Tellurium displays a distorted dodecahedral stereochemistry formed by two interposing trapezoids, one resulting from the four sulphurs of two L groups and the other from the two sulphurs of the third L and the two oxygens of the perchlorate ion. The average TeS distance 2.648(2) Å is close to that reported in other tris(dithiocarbamato)tellurium(IV) complexes. The perchlorate is weakly coordinated to tellurium(IV), with the average TeO distance being 2.994(8) Å. The unusual coordination of perchlorate (as a bidentate ligand) to tellurium(IV) dithiocarbamate is reported for the first time.     

The crystal structure of hydrogen cerium(III) sulfate hydrate, [H3O][Ce(SO4)2] · H2O

[H₃O][Ce(SO₄)₂] · H₂O crystallizes in the monoclinic system with unit-cell dimensions (from single-crystal data) a = 9.359(4), b = 9.926(4), c = 8.444(3) Å, β = 96.53(9)° and space group P2₁/n, z = 4. The structure was solved by conventional heavy-atom methods using 1787 counter-measured reflections (MoKα radiation), and refined using full-matrix least-squares techniques to an R of 0.0465 (ωR = 0.0413). The structure consists of cerium(III) ions in irregular nine-coordination to oxygen atoms from two bidentate sulfate ions, four monodentate sulfate oxygen atoms, and one water molecule. The oxonium ions are present as isolated ions in the structure and take par in the hydrogen bonding network. The Ce-O bond lengths range from 2.454(7) to 2.626(6) Å.     

Neutron diffraction study of UO2SeO4 · 2D2O

A powdered sample of deuterated uranyl selenate dihydrate UO₂SeO₄ · 2D₂O is studied by neutron diffraction. This compound crystallizes in monoclinic space group P2₁/c; a = 6.974(1) Å, b= 8.289(2) Å, c = 11.664(2) Å, β=92.319(6)°, Z = 4, R _f = 3.14, R _I = 5.53, gC² = 2.82. The main structural units of the compound are [UO₂SeO₄(D₂O)₂] chains propagating along [100]. These chains are linked into a framework group (A = UO ₂ ²⁺ , T³ = SeO ₄ ^2? , and M¹ = D₂O) of uranyl complexes. These chains are linked into a framework by a system of hydrogen bonds formed by water hydrogen atoms of one chain and uranyl oxygen atoms of another.