Diffusion aspects of lithium intercalation as applied to the development of electrode materials for lithium-ion batteries

The creation of new electrode materials and the modification of existing ones are important trends in the development of lithium-ion batteries. Of special significance is to evaluate their diffusivity, i.e., the ability of providing transfer of the electroactive component. Such electrochemical techniques as cyclic voltammetry, electrochemical impedance spectroscopy, potentiostatic intermittent titration technique, and galvanostatic intermittent titration technique are used for this purpose. The values of chemical diffusion coefficient D estimated in similar electrode materials are shown to scatter by several orders of magnitude. Principal causes of this rather considerable scattering are discussed, including the uncertainty of diffusion area estimations and the use of various approaches to deriving equations to calculate D. Our conclusions are illustrated by examples of D estimations in the electrode materials Li _x C₆, Li _x Sn, Li _x TiO₂, Li _x WO₃, LiM _y Mn_2?y O₄, and LiFePO₄.     

The structure of the dithionite ion

The Raman spectra of aqueous and solid sodium dithionite have been recorded. Differences in the location, intensity, and number of observed bands are attributed to conformational changes in the dithionite ion. The structure of the aqueous ion is non-planar with a C_2h symmetry with an SS bond distance estimated to be 0.220–0.226 nm, as opposed to the dithionite structure in the Na₂S₂O₄·2H₂O salt which is known to have C_2ν structure with a bond distance of 0.2389 nm. The Raman spectra of aqueous dithionite are assigned to A_g (SO) = 997 cm^?1; B_g (SO) at 912 cm^?1, B_g SO₂ twist at 324 cm^?1. The remaining bands are a strong A_g, the SO₂ wag, the SO₂ scissor, and the SS stretch at 584, 461, and 232 cm^?1, respectively, but due to coupling all three motions are expected to exhibit substantial SS character. The variation of the spectra of the solid and aqueous sodium dithionite indicate strong environmental effect on the structure of the anion.     

Calculation of the rotational magnetic moments of the ammonia and water molecules

We calculate the rotational magnetic moments and the corresponding g-factors for water and ammonia. Our results are g_xx = 0.397, g_yy = 0.769 and _zz = 0.345 for water and g_xx = g_yy = 0.69 and g_zz = 0.51 for ammonia. The experimental values are g_xx = 0.585, g_yy = 0.742 and g_zz = 0.666 for water and g_xx = g_yy = 0.56 and g_zz = 0.484 for ammonia.     

Quantitative estimation of the discontinuous function of the solvent in aqueous electrolyte solutions

The adiabatic compression method is used to determine quantitative solvation parameters such as hydration numbers h, the molar adiabatic compressibility of hydrated complexes β _h V _h , the volume V _1h and compressibility β_1h of water in ion hydration shells, and several other properties in the temperature range 278.15–323.15 K. Hydration numbers are used to determine the verified activity coefficient of the solvent, γ _R . The concentration dependence of the coefficient is shown to be a discontinuous function, with the discontinuity point corresponding to the complete solvation boundary.     

Evaluation of several literature equations to predict the vaporization enthalpies at the normal boiling point

Some literature relations proposed by Vetere are re-examined to simplify their analytical form and to improve their performances. Moreover, their results are compared with those of three literature equations by Riedel, Chen and Liu. Four equations include universal parameters, which can be used for any type of compounds and, to be applied, only require the knowledge of the normal boiling temperature T_b, and of the critical constants T_c and P_c. Other six equations are purely empirical, since they are not based on the corresponding state principle: three of them are function of T_b and of the molecular weight M, while the last three equations need M and the polarity parameter W_p. The parameters of the equations that disregard the use of the critical constants are to be optimised separately for three classes of compounds, namely hydrocarbons, polar compounds and alcohols. Moreover, to have a severe test, nearly 290 experimental data of ΔH_vb were processed, chosen from the most reliable reported in the fifth edition of the properties of gases and liquids.     

The influence of the crystal lattice structure on the conduction band energy of oxides of titanium(IV)

The reducing properties of conduction band electrons of anatase, rutile and strontium titanate were correlated with their structures. It was shown by extended Hückel MO calculations on model complexes that the energy levels of the lowest unoccupied molecular orbitals (LUMOs) involving predominantly the 3d_τ orbitals xy, xz and yz of Ti are sensitive to the lattice structure. The calculated LUMO energies are in qualitative agreement with experimental flat-band potentials (E_1b) and band-gap energies (E_g). The presently unknown E_g and E_1b of brookite are estimated as 3.14 eV and = −0.03 V versus NHE, respectively. These values are intermediate between anatase and rutile.     

Raman spectra of the polymeric difluorides of the group IV elements and the structure of polydifluorosilylene

The Raman spectra for (SiF₂)_x and GeF₂ are reported. In the spectrum of (SiF₂)_x a band has been observed at 411 cm⁻¹ and is most probably associated with SiSi bonding in the compound; this is the first direct evidence for such a bond. The high degree of similarity between the spectra of (SiF₂)_x and (CF₂)_x suggests that (SiF₂)_x is a zig-zag helical chain polymer similar to (CF₂)_x.     

Differential scanning calorimetry study of the thermal decomposition of peroxides in the absence of a solvent

The thermal decompositions of benzoyl peroxide (Bz₂O₂), dicumyl peroxide (DICUP) and α, α′-bis (t-butylperoxy)m/p-diisopropylbenzene (Peroximon F) in the absence of solvents have been studied by means ofDSC alone. The DSC curves allowed calculation of the half-lifetime (t _1/2) and the time (t ₁) required to decompose the whole of the peroxides. Thet ₁, andt _1/2 values found for the pure peroxides are lower than those in the literature for decomposition in solution. The heat of decomposition and the activation energy for each peroxide are reported.     

Mathermatical modeling of equilibria and the state of holmium heteropoly tungstate ions

The interaction in the HoW₁₀O ₃₆ ^9? -H⁺-OH^?-H₂O system is studied using pH titration at cH0W₁₀O ₃₆ ^9? = 10^?3 mol/l in various base electrolytes (NaNO₃, NaCl, Na₂SO₄). The pH titration data are used to simulate the processes in the solution in ranges of z _H ⁺ = 0?6.5 and z _OH ⁺ = (?4)-0. The concentration and thermodynamic equilibrium constants are calculated, and heteropolytungstate anion (HPTA) distribution diagrams are plotted. Thallium salts are synthesized in the regions of dominant existence of heteropoly anions H_nHoW₁₀O ₃₆ ^(9?n)? (n = 2?4). The compounds are identified using chemical analysis and IR spectroscopy.     

On the influence of spatial correlations on the rate of chemical reactions in dense systems. II. Numerical results

The explicit expressions for the rate constant k_f and k_b of a dense system obtained in the preceding paper are investigated numerically. The pair correlation functions representing the spatial correlations are calculated from an associate nonreactive hard sphere system by means of the multicomponent Percus—Yevick equation. The rate constants are found to differ in their dependence on density and time up to an order of magnitude from the corresponding dilute gas value. The time behaviour of k_f and k_b was found to depend sensitively on a relation between the total volumes of the reactant and product molecules.     

Effect of isomeric butanols on the temperature corresponding to the adiabatic compressibility minimum of water

The effect of isomeric butanols on the temperature corresponding to the adiabatic compressibility minimum of water (T _β) was studied using a variablepath interferometer working at 3 MHz. The structural contribution to the shift inT _β, [ΔT _βstr]_exp, was found to be positive and to increase with concentration to a maximum atX ₂?0.0193, 0.0100, and 0.0090 fort-butanol, sec-butanol, and isobutanol, respectively. The results have been explained on the basis of stabilization of water structure at low concentrations of alcohol. The quantity [ΔT _βstr]_exp forn-butanol is practically zero at low concentrations, while at high concentrations it is negative, indicating rupture of the hydrogen-bonded structure of water by this solute. At any given concentration,t-butanol > sec-butanol > isobutanol >n-butanol is the order of increasing structural contribution to the shift inT _β. Theoretical values of the structural contribution to the shift inT _β are in good agreement with the experimental data.     

Derivatives of cyclooctatetraenecyclopentadienyl-titanium containing substituents in the five-membered ring

The syntheses of some substituted cyclooctatetraenecyclopentadienyl-titanium compounds are described, viz: (h⁸-C₈H₈)(h⁵-R)Ti with R = C₅H₄CH₃, C₅H₄C(CH₃)₃, C₅H₄Si(CH₃)₃, indenyl (= Ind) and fluorenyl (= Flu). The compounds have been prepared by reaction of [(h⁸-C₈H₈)TiCl·THF]₂ with RNa in ether solution. The paramagnetic compounds are thermally stable to ca. 350°, but they are sensitive to air and water. The IR spectra and dipole moments of the compounds are given. The mass spectra of the complexes (h⁸-C₈H₈)(h⁵-C₅H₅)Ti, (h⁸-C₈H₈)(h⁵-Ind)Ti and (h⁸-C₈H₈)(h⁵-Flu)Ti indicate weakening of the Tih⁵R bond-strength in this sequence.     

Features of the kinetics of the liquid-phase oxidation of cyclohexanol

The kinetics of oxygen uptake in the cumyl peroxide-initiated oxidation of cyclohexanol (373 K, o-dichlorobenzene) is studied. The parameters of the oxidizability of k _p (2k _t )^?0.5 (which depend on [RH]) and the rate constants of the bi- and trimolecular reactions of chain initiation (k ₀ = 1.25 × 10^?8 L/(mol s) and k′₀ = 2.5 × 10^?9 L²/(mol² s), respectively) are determined by solving the inverse kinetic problem. It is demonstrated that the quadratic-law recombination of peroxyl radicals during cyclohexanol oxidation also occurs without chain termination. The recombination rates of peroxyl radicals with and without chain termination (k′/k _t ) are found to grow with increasing [RH], reaching their maxima at [RH] = 1.0 mol/L, and to diminish subsequently. We conclude that this can be attributed to changes in the ratio between the propagating peroxyl radicals (hydroperoxyl and 1-hydroxycyclohexylperoxyl) in the reaction medium.     

Compositions of the shells of nanoparticles with pentagonal symmetry

A method of calculation of the number of atoms in the structure of nanoforms with pentagonal symmetry (fullerenes, nanoparticles, clusters) depending on the arrangement of atoms on the symmetry elements of the I _h group has been developed. The formulas for calculation of the number of particles in all possible shells, including multilayer ones, are reported. The numbers of atoms in the shells of pentagonal symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of all possible atomic shells S _{? + 60z} (z = 0, 1, ...) is presented, and the constructions of the basic shells S _? (? = 12, 20, 30, 50, 60) are given. For each basic shell, the sum rule is met: the sum of the coordination numbers of the elements of subshells is equal to 60. In clusters with magic numbers, basic shells are periodically repeated. In addition to the known shells of nanostructures, the formulas of new structures that are expected to be stable—B₂₀O₃₀, B₆₀O₉₀ (B₂O₃), and B₉₀O ₁₃₀ ¹⁰⁺ (borate)—are reported for the first time. The same is valid for similar compounds of Group III elements.     

The scavenging of the precursors of the solvated electron from the positron lifetime spectroscopy and the doppler broadening of annihilation line shape technique

The electron scavenging properties of aqueous solutions of two series of solutes are investigated, using the positron as a probe. For a better interpretation of the data, both lifetime spectroscopy and the Doppler broadening of annihilation line shape technique are used. All solutes inhibit the positronium (Ps) formation, by the scavenging of electrons. The first series consists of the halate ions, that should follow the Hunt linear relation between the rate constant for reaction with the solvated electrons, k_(e^?aq+S), and that for its precursor(s), 1/C₃₇. The Ps inhibition constants, k, are 0.14, 1.44 and 3.45 M^?1 for ClO^?₃, BrO^?₃ and IO^?₃, respectively. This sequence is quantitatively consistent with that of the respective k_(e^?eq+S). The second series includes the SeO⁼₄, Te(OH)₆ and BrO^?₄ species, and the Ps inhibition constants are 5.62, 10.5 and 14.3 M^?1 respectively. These values are much higher than expected from the k_(e^?aq+S) constants, on basis of the Hunt relation, in agreement with previous results from pulse radiolysis experimets.     

A mechanistic study of the acid- and base-catalysed cleavages of β-trimethylstannylstyrenes

The cleavages of cis- and trans-PhCHCHSnMe₃ in 1/10 AcOD-MeOD have been shown to give cis- and trans-PhCHCHD, respectively. The rates of cleavage of some XC₆H₄CHCHSnMe₃ compounds in 1/10 AcOH-MeOH at 50°C have been measured; there is no significant difference between the rates for cis- and trans-PhCHCHSnMe₃, and the relative rates of cleavage as X is varied are (X  H), 1.0; p-OMe, 7.0; p-Me, 2.3; m-Cl, 0.34; m-Br, 0.36. There is an excellent correlation with σ⁺ constants, with a ρ value of 1.1. The results are interpreted in terms of rate-determining proton transfer to the β-carbon atoms, and it is suggested that acid cleavages of vinylHgX bonds involve analogous mechanisms. PhSnMe₃ is cleaved 20 times as slowly as PhCHCHSnMe₃ in the 1/10 AcOH/MeOH.The rates of cleavage of XC₆H₄CHCHSnMe₃ compounds by a mixture of MeOH (3 vol.) and 2 M aqueous NaOH (2 vol.) have been measured; trans-PhCHCHSnMe₃ is cleaved about 1.3 times as rapidly as its cis-isomer, and about 12 times as rapidly as a mixture of cis- and trans-PhCHCHSnEt₃. The relative rates for the various XC₆H₄CHCHSnMe₃ compounds (mainly trans-isomers) are (X ) H, 1.0; p-OMe, 0.99; p-Me, 0.92; m-Cl, 1.67; m-Br, 1.65. Cleavage of trans-PhCHCHSnMe₃ by NaOD/D₂O/MeOD gives exclusively trans-PhCHCHD. For cleavages in methanolic NaOMe the values of the rate isotope effects, (the ratio k_meOH/k_MeOD) are 2.3–2.6, and those of the product isotope effects, PIE (the product ratio RH/RD on cleavage of RSnMe₃ by NaOMe in 1 : 1 MeOH/MeOD) are 4.5–5.0.The results are interpreted in terms of proton transfer from the solvent to the leaving carbon atom in the rate determining step as the SnC bond breaks as a result of the attack of the base anion at tin in a prior or synchronous process. PhCHCHSnMe₃ is cleaved by the aqueous alcoholic base about 5 times as rapidly as PhSnMe₃.Cleavage of trans-PhCHCHSnMe₃ by PHCOCl in presence of AlCl₃ in CH₂Cl₂ gives trans-PhCHCHCOPh, and cleavage of a 90/10 mixture of trans- and cis-PhCHCHSnMe₃ by bromine in CCl₄ gives a corresponding mixture of trans- and cis-PhCHCHBr.     

A MALDI mass spectrometry investigation of the compositions of the products of the partial acidolysis of MeSi(OMe)3

The molecular-mass compositions of the products of partial acidohydrolytic polycondensation that are formed during the interaction of MeSi(OMe)₃ with CH₃COOH have been studied via MALDI mass spectrometry. It has been shown that, depending on the molar ratio of MeSi(OMe)₃ and CH₃COOH (m/n), a wide range of oligomethylmethoxysiloxanes with the average composition [MeSiO _n/m (OMe)_{(3 ? 2n/m)}] _p are formed. The analysis of molecular masses and ²⁹Si NMR spectra of the products has revealed various types of molecular structures, which change from linear, branched, and cyclic to polycyclic clusters with condensed cycles after a change in the degree of polycondensation α = 100 × [2n/3m] from 66.67 to 83.33%. At a degree of polycondensation of α = 86.67% or higher, the polycyclic clusters form a spatially crosslinked structure (gel).     

Comparative analysis of the state of lithium and sodium atoms in water clusters

Structures and energetic characteristics of Li(H₂O) _n and Li⁺(H₂O) _n clusters with n = 1–6, 19, and 27 determined in the second order of the Møller-Plesset perturbation theory with 6–31++G(d,p) basis set are analyzed. The electron density redistribution, which takes place upon the electron addition to a Li⁺(H₂O) _n cluster, is found to be provided by hydrogen-bonded water molecules: initially almost neutral molecules, which are most distant from lithium, become negatively charged. The calculated energies of the electron capture by Li⁺(H₂O) _n clusters are approximated with the appropriate electrostatic model, and estimates of the lithium ionization energy in water clusters of various sizes are found. Similar estimates obtained earlier for sodium are made more accurate.