Inclusion of the concentration dependence of the diffusion coefficient in the sand equation

The applications of the Sand equation in potentiometry of electrode and membrane systems for precise measurements of the transition time (τ) have been determined. An approach was suggested for choosing the diffusion coefficient of electrolyte (D) in the case when the concentration changes from its value in the agitated solution (where D = D_b) to the nearly zero value at the surface (D = D₀ corresponds to an infinitely dilute solution), D_b and D₀ being substantially different. The Nernst–Planck–Poisson nonstationary equations were numerically solved in a one-dimensional system including an ion-exchange membrane and two adjacent diffusion layers (for the electrode–solution system, the result is a particular case). An effective value D_ef was found, whose substitution in the Sand equation gave τ identical to that obtained by numerical solution. The neglect of the concentration dependence D(с) can lead to a nonadequate determination of the ion transport numbers in the membrane.     

Electron affinity and substituent effects in radical anions

The first vertical electron affinities EA of 13 series of molecules and free radicals D(X _i ) _n are related to the inductive (σ _I ), resonance (σ _R ^? ), and polarization (σ_α) parameters of substituents X _i by the dependences EA = EA _H + aΣσ _I + bΣσ _R/? + cΣσ_α: In radical anions D^+·(X _i ) _n , compared to radical cations D^+·(X _i ) _n , the polarization interaction is weaker or similar in magnitude but has an opposite sign. The previously unknown resonance parameters σ _R ^? of substituents SiMe₃ and CH₂SiMe₃ bound to the radical anion center H₂C=CH^?· were calculated.     

Oxygen isotope exchange in praseodymium nickelate

Oxygen surface exchange kinetics and diffusion were studied in Pr₂NiO_4?+?δ (PNO) by the isotope exchange method with gas phase equilibration in the temperature range of 600–800 °C and oxygen pressure range of 0.33–1.62 kPa. The oxygen heterogeneous exchange rate (r_H), oxygen diffusion coefficient (D), rates of oxygen dissociative adsorption (r_a), and oxygen incorporation (r_i) were calculated along with the apparent activation energies of oxygen surface exchange and diffusion processes. The temperature dependence of r_H was found to benon-linear in Arrhenius coordinates. The apparent activation energy changed from 1.4?±?0.2 eV at T?>?700 °C to 2.0?±?0.1 eV. This might be attributed to the change in the rate-determining stage of oxygen exchange for Pr₂NiO_4?+?δ at T ~?700 °C, because of a shift in the ratio between r_a and r_i caused by the difference in their activation energies. Possible reasons for the observed changes in the rate-determining stage are discussed.     

<Emphasis Type="Italic">Ab initio</Emphasis> study of scandium fluoride molecules: ScF,ScF<Subscript>2</Subscript>, AND ScF<Subscript>3</Subscript>

Equilibrium geometric parameters, normal mode frequencies and intensities in IR spectra, atomization enthalpy, and relative energies of low-lying electronic states of scandium fluoride molecules (ScF, ScF₂, and ScF₃) are calculated by the coupled-cluster method (CCSD(T)) in triple-, quadruple, and quintuple-zeta basis sets with the subsequent extrapolation of the calculation results to the complete basis set limit. The ScF molecule is also studied by the CCSDT technique. The error in the approximate calculation of triple excitations in the CCSD(T) method does not exceed 0.002 Å for the equilibrium internuclear distance R _e, 4 cm^?1 for the vibrational frequency, and 0.2 kcal/mol for the dissociation energy of the molecule. In the ground electronic state \(\tilde X^2 \) A ₁(C _2ν ) of ScF₂ molecules, R _e(Sc-F) = 1.827 Å and α_e(F-Sc-F) = 124.2°; the energy barrier to bending (linearization) h = E _min(D _g8h ) ? E _min(C_2ν) = 1652 cm^?1. The relative energies of Ã²Δ _g and \(\tilde B^2 \)Π _g electronic states are 3522 cm^?1 and 14633 cm^?1 respectively. The bond distance in the ScF₃ molecule (\(\tilde X^1 \) A′₁, D _3h ) is refined: R _e(Sc-F) = 1.842 Å. The atomization enthalpies Δ_at H ₂₉₈ ⁰ of ScF _k molecules are 139.9 kcal/mol, 289.0 kcal/mol, and 444.8 kcal/mol for k = 1, 2, 3 respectively.     

Standard Thermodynamic Functions of Crystalline Arsenate Mg<Subscript>0.5</Subscript>Zr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript> in the Range from <Emphasis Type="Italic">T</Emphasis> → 0 to 670 K

The temperature dependence of heat capacity C^° _p = f(T) of crystalline arsenate Mg_0.5Zr₂(AsO₄)₃ was studied by precision adiabatic vacuum and differential scanning calorimetry in the temperature range 8?670 K. The standard thermodynamic functions C^° _p (T), H°(T)–H°(0), S°(T), and G°(T)–H°(0) of the arsenate for the range from Т → 0 to 670 K and the standard formation entropy at Т = 298.15 K were calculated from the obtained experimental data. Based on the low-temperature capacity data (30–50 K) the fractal dimension D of the arsenate was determined, and the topology of its structure was characterized. The results were compared with the thermodynamic data for the structurally related crystalline phosphates M_0.5Zr₂(PO₄)₃ (M = Mg, Ca, Sr, Ba, Ni) and arsenate NaZr₂(AsO₄)₃.     

Properties of solvate shells and the mobility of ions,according to molecular dynamics data

The solvate shells of an ion, its velocity autocorrelation function, and diffusion coefficient D are found, and the interrelations between them are analyzed. A single ion in the system of atoms of a liquid is considered a model system. The interaction between the ion and atoms of the liquid is described by polarization potential U(r); the interaction between atoms of the liquid alone is described by the Lennard–Jones potential. A classical molecular dynamics method is used. Five solvate shells around the ion are found, and the lifetimes of atoms on each shell are calculated. It is found that the velocity autocorrelation function is of a vibrating nature. The spectrum of the autocorrelator and the frequency of cluster vibrations in a linear approximation are compared. Dependences D on parameters of potential U(r) are found. No dependence D on the ion mass is found; this is explained by solvation. The Einstein–Stokes formula and the HSK approximation are used in discussing the results. It is shown that at small radii of the ion, dependence D on parameters U(r) is described by such a model. When the ion radius is increased, the deviation from this dependence and an increase in D are observed. The results are compared to experimental mobilities of O₂^- and Ar₂⁺ ions in liquid argon.     

Determination of sorption and diffusion parameters of <Superscript>99</Superscript>Tc in crushed granite using through-diffusion experiments

Diffusion and sorption are important processes associated with radionuclides migration in crystalline rock. These processes are studied in the laboratory using borehole core samples. In this study, we obtained distribution coefficients (K _d), apparent diffusion coefficients (D _a) and retardation factor (R _f) using batch and through-diffusion experiments. The \( R_{\text{f}}^{\text{H/Tc}} \) and \( K_{\text{d}}^{\text{H/Tc}} \) values obtained using the accumulative concentration method were lower than those derived in the batch experiments. These findings demonstrate that reliable R _f and K _d values of ⁹⁹Tc can be obtained using through-diffusion experiments with a non-reactive radiotracer, thereby bolstering confidence in the assessment of the long-term performance of disposal repositories.     

Thermodynamic Properties of Polyphenylquinoxaline in the Temperature Range of <Emphasis Type="Italic">T</Emphasis> → 0 to 570 K

The thermodynamic properties of amorphous polyphenylquinoxaline in the temperature range of 6 to 570 K are studied via precision adiabatic vacuum calorimetry and differential scanning calorimetry. The thermodynamic characteristics of glass transition are determined. Standard thermodynamic functions C^°_p, H°(T) ? H°(0), S°(Т) ? S°(0), and G°(T) ? H°(0) in the range of T → 0 to 570 K and the standard entropy of formation at T = 298.15 K are calculated. The low-temperature (T ≤ 50 K) heat capacity is analyzed using a multifractal model for the processing of heat capacity, fractal dimension D values are determined, and conclusions on the topological structure of the compound are drawn.     

Structure and energetics of β-diketonates. XVI. Molecular structure and vibrational spectrum of zinc acetylacetonate according to gas-phase electron diffraction and quantum-chemical calculations

The molecular structure of zinc acetylacetonate was studied in a simultaneous electron diffraction and mass spectrometric experiment at 376(7) K and by quantum-chemical calculations. The Zn(acac)₂ molecule has a structure of D _2d symmetry with the chelate rings lying in mutually perpendicular planes. The main geometrical parameters of the molecule are r _h1(Zn-O) = 1.942(4) Å, r _h1(C-O) = 1.279(3) Å, r _h1(C-C_r) = 1.398(3) Å, r _h1(C-C _m ) = 1.504(5) Å, ∠(O-Zn-O) = 93.2(7)°, ∠(Zn-O-C) = 125.9(7)°, ∠(C-C_r-C) = 125.8(14)°, ∠(O-C-C _m ) = 115.2(9)°. The effective rotation angle of methyl groups is close to 30°, which is indicative of the free rotation of these groups. The vibration frequencies were obtained by quantumchemical calculations, and the IR spectrum of the Zn(acac)₂ molecule was interpreted.     

Measurement and Modeling the Excess Molar Volumes and Refractive Index Deviations of Binary Mixtures of 2-Propanol, 2-Butanol and 2-Pentanol with <Emphasis Type="Italic">N</Emphasis>-Propylamine

The densities, ρ, and refractive indices, n _D, of 2-alkanols (C₃–C₅) with N-propylamine have been measured for the whole range of composition at temperatures from (298.15–328.15) K at 10 K intervals and ambient pressure of 81.5 kPa, using an Anton Paar DMA 4500 oscillating tube densimeter and an Anton Paar Abbemat 500 automatic refractometer. From the experimental data, excess molar volumes \( V_{\text{m}}^{\text{E}} \) partial molar volumes \( \bar{V}_{i} \) apparent molar volumes V _?i and refractive index deviations Δn _D the binary systems consisting of N-propylamine + 2-alkanols (2-propanol, 2-butanol, 2-pentanol) were calculated and \( V_{\text{m}}^{\text{E}} \) and Δn _D values were correlated with the Redlich–Kister polynomial. The effect of temperature and the chain length of the alcohol on the excess molar volumes and refractive index deviations are discussed in terms of molecular interaction between unlike molecules. The excess molar volumes are negative and refractive index deviations are positive over the entire composition range, which indicates strong hydrogen bonding between molecules of the mixtures. A comparative study has been made of the refractive indices obtained experimentally and those calculated by means of the Lorentz–Lorenz, Weiner and Arago–Biot relations. The perturbed chain statistical associating fluid theory (PC-SAFT), simplified PC-SAFT and Prigogine–Flory–Patterson theory were also applied to correlate and predict the density and excess molar volumes of the mixtures.     

Synthesis and heat capacity of NdVO<Subscript>4</Subscript> in the temperature range of 384–859 K

Heat capacity of NdVO₄ was determined in the temperature range of 384–859 K using differential scanning calorimetry. The thermodynamic functions (H°(T)–H°(384 K), S°(T)–S°(384 K), and Φ°) of neodymium orthovanadate were calculated using the experimental C_p = f(T) values. The structure of NdVO₄ was studied at 298 and 973 K.     

Structure and dynamics of a free aquaporin (AQP1) by a coarse-grained Monte Carlo simulation

Structure and dynamics of a free aquaporin (AQP1) are studied by a coarse-grained Monte Carlo simulation as a function of temperature using a phenomenological potential with the input of a knowledge-based residue–residue interaction. Response of the radius of gyration (R _g) of the protein to the temperature (T) is found to be nonlinear: Decay of R _g at T ≤ T _c is followed by a continuous increase at T ≥ T _c before reaching its saturation. In thermo-responsive regime, the protein exhibits segmental globularization with the persistence of three regions along its sequence involving residues ¹M–²⁵V and ²⁵⁰V–²⁶⁹K toward the beginning and end segments with a narrow intermediate region around ¹⁵⁵A–¹⁶³D. A detail analysis of the structure factor S(q) shows a global random coil conformation at high temperatures with an effective dimension D _e ~ 1.74 and a globular structure (D _e ~ 3) at low temperatures. In thermo-responsive regime, the variation of S(q) with the wave vector q reveals a systematic redistribution of self-organizing residues (in globular and fibrous sections) that depends on the length scale and the temperature.     

Evaluation of the probability of reaction of fast oxygen atoms with polymers and graphite

On the basis of analysis of published data on the reaction efficiency of various polymer materials and graphite in their interaction with fast oxygen atoms (energy of about 4.5 eV) as obtained in flight tests of materials in low-Earth orbits of the International Space Station and ground tests, probability P _r of chemical oxidation reactions accompanied by ablation has been evaluated. Estimates have been made for 33 polymers consisting of carbon, hydrogen, oxygen, and nitrogen and graphite for two extreme cases when the carboncontaining oxidation products are either CO or CO₂ alone. The average probability values found are P _r(CO)(av) = 0.184 and P _r(CO₂)(av) = 0.317. The probability values range from P _r(CO) = 0.604 and P _r(CO₂) = 0.963 for allyl diglycol carbonate to P _r(CO) = 0.038 and P _r(CO₂) = 0.075 for pyrolytic graphite.     

Model-free temperature scaling for heat capacity

In treating the experimental data on the heat capacity of solids, the essence of any model application is in the searching for the scaling factors (k _i or 1/Θ_i) which transform a set of independent functions C _P,i(T) for every substance into a function C _P(T·k _i) universal for the particular set of substances. DSC heat capacities of I–III–VI₂ compounds at elevated temperatures exceed the upper limit of 12R (3R per mole of atoms) and make impossible application of any model. Nevertheless, the temperature scaling of heat capacity can be solved as a pure mathematical problem without any physical model (theory). The benefits of the model-free scaling are illustrated with the case of four isostructural chalcogenides (LiInS₂, LiInSe₂, LiGaS₂, and LiGaSe₂) measured recently with DSC in a temperature range from 180 to 460 K. The upper limit of C _P(T·k _i) functions was expanded up to 635 K. Low-temperature heat capacity of LiInSe₂ published in 1995 made it possible to derive the thermodynamic functions (enthalpy and entropy) for LiInS₂ (0–590 K), LiGaS₂ (0–640 K), and LiGaSe₂ (0–490 K) and expand those data for LiInSe₂ from 300 to 460 K.     

Molecular dynamics simulations of the characteristics of sodium carboxymethyl cellulose with different degrees of substitution in a salt solution

Sodium carboxymethyl cellulose (SCMC) with different degrees of substitution (DS) possesses structural characteristics and physicochemical properties that are important in broad areas of industrial applications. This reported work investigated the structural characteristics, including the effective length (L _ef), the radius of gyration (R _g), and the hydrodynamic radius (R _H), and the physicochemical properties, including intrinsic viscosity ([η]) and salt tolerance, of SCMC with a DS more than 1.0 in NaCl solution using molecular dynamics (MD) simulations. In the MD simulations, the DS of SCMC varied from 1.2 to 2.8, and the NaCl concentration varied from 0 to 1.4 mol/L. MD simulation results showed that with the increment of NaCl concentration, the L _ef (or R _g or R _H) of SCMC decreased; with the increment of the DS, the L _ef of SCMC increased. Also, the variation tendency of [η] in the NaCl solution was consistent with its L _ef (or R _g or R _H). It was noted that the salt tolerance (represented by D) of SCMC increased as the DS increased. In addition, the sharp variation of the D value of SCMC occurred in the range of DS of 1.6 to 2.0, which agreed with the reported experimental results. Radial distribution function analyses showed that the Na⁺ cations had a stronger interaction with the carboxyl groups in SCMC with lower DS when it was present in a salt solution of higher concentration, which also reasonably explained the variation of L _ef, R _g, R _H, [η], and D of SCMC in NaCl solution.     

Nanocrystalline Calcium Carbonate Hydroxyapatites Containing Multiwall Carbon Nanotubes: Synthesis and Physicochemical Characterization

Nanocomposites (NCs) based on carbonated calcium hydroxyapatite (CHA) (bioapatite, an analogue of the inorganic component of mammalian bone tissue), carbonate apatite (Ca₁₀(PO₄)₆CO₃, CA), and multiwall carbon nanotubes (CNTs) are prepared in the system CaCl₂–(NH₄)₂HPO₄–NH₄HCO₃–NH₃–CNT–H₂O (25°C) by coprecipitation of calcium and phosphorus salts with CNTs from aqueous solutions. The physicochemical properties of nanocomposites are studied as dependent on their formation conditions and composition using the solubility (residual concentrations) method and pH measurements. The composition, crystal structure, morphology, spectroscopic and thermal characteristics of the synthesized CHA/CNT and CA/CNT NCs are determined using chemical analysis, X-ray powder diffraction, thermal analysis, and IR spectroscopy. Either CHA/CNT NCs of composition Ca₁₀(PO₄)₆(CO₃)_x(OH)_2–2х · yCNT · zH₂O, where х = 0.2; 0.5; 0.8; y = 1, 2, 3; z = 6.8–10.8, or (when х = 1) CA/CNT NCs of composition Ca₁₀(PO₄)₆CO₃ · yCNT · zH₂O, where y = 1–3; z = 6.9–10.8, are formed as the carbonate and CNT contents of the NC increase. Our results favor the understanding of the effect of carbonization and CNTs on the metabolic formation of native bone tissue apatite and can be used for the design of efficient ceramics for bone implants.     

Structural studies of nickel(II) complexes with 1-<Emphasis Type="Italic">tert</Emphasis>-butylimidazole-2-thione and 3-phenyl-5-methyl-pyrazole ligands

The nickel(II) complexes dichlorobis(1-tert-butylimidazole-2-thione)nickel(II) [Ni(tm ^t-Bu)₂Cl₂] (1), dinitratobis(1-tert-butylimidazole-2-thione)nickel(II) [Ni(tm ^t-Bu)₂(NO₃)₂] (2), dichloro-bis(3-phenyl-5-methyl-pyrazole)(1-tert-butylimidazole-2-thione)nickel(II) [Ni(pz^Ph,MeH)₂(tm ^t-Bu)Cl₂] (3) and dinitratobis(3-phenyl-5-methyl-pyrazole)(1-tert-butylimidazole-2-thione)nickel(II) [Ni(pz^Ph,MeH)₂(tm ^t-Bu)(NO₃)₂] (4) have been synthesized and studied. The single crystal X-ray diffraction analysis was carried out for 1 and 4 {Bruker Kappa Apex-II CCD diffractometer, MoK _α radiation}. Crystal data for 1: monoclinic C2/c, a = 16.949(2) Å, b = 8.6647(10) Å, c = 15.461(3) Å, β = 117.662(4)°, V = 2011.1(5) ų, Z = 4, D _calc = 1.460 g/cm³. Crystal data for 4: triclinic P-1, a = 9.9775(7) Å, b = 11.2254(8) Å, c = 14.8068(10) Å, α = 75.401(4)°, β = 87.422(4)°, γ = 74.874(4)°, V = 1548.86(19) ų, Z = 2, D _calc = 1.405 g/cm³. Coordination core of complex 1 adopts distorted tetrahedral geometry whereas core 4 has distorted octahedral geometry. The bonded nitrates are of two types coordinating as monodentate and bidentate ligands.     

Molecular dynamics simulation of the structure and thermodynamic properties of liquid rubidium at pressures of up to 10 GPa and temperatures of up to 3500 K

The models of rubidium at temperatures of up to 3500 K, degrees of compression of up to Y = V/V₀ = 0.3, and pressures of up to 32 GPa were constructed by molecular dynamics (MD) using the interparticle potential ЕАМ. The thermodynamic properties of the MD models agree satisfactorily with experiment in the range of parameters under study at rubidium densities higher than 0.86 g/cm³. The behavior of the models in the range of the van der Waals loop was analyzed; the calculated critical temperature of rubidium T_c is ～2250 ± 25 K, density ～0.41 g/cm³, pressure ～0.019 GPa, and compressibility factor Z = pV/RT ≈ 0.137. The states with the unity factor Z = 1 were observed at pressures of up to 0.30 GPa (at ～3000 K); the temperature dependence of the density of the models with Z = 1 is nearly linear, and the Boyle temperature is T_B ≈ 10160 K. The ratio T_c/T_B = 0.221 is close to this value for cesium (0.23) and mercury (0.276). In the temperature and pressure ranges under study, the inversion of the Joule–Thomson coefficient did not take place, but should be observed at pressures of ?0.3 GPa and elevated temperatures. It was found that the diffusion coefficient D(T) dependences do not straighten in the usually used coordinates within wide temperature ranges. It was concluded that the structure of the liquid smoothly changes when the rubidium models are compressed and this reveals in the change of the degree of asymmetry of the first peak of the radial distribution function.     

Apparent Molar Volumes of Aqueous Solutions of Magnesium Tetraborate from 283.15 to 363.15 K and 0.1 MPa

Densities for aqueous solutions of magnesium tetraborate MgB₄O₇(aq) at the molalities of (0.00556–0.03341) mol·kg^?1 were measured with an Anton Paar Digital vibrating-tube densimeter at temperature intervals of 5 K from 283.15 to 363.15 K and 0.1 MPa. Apparent molar volumes were obtained based on the experimental density data, and the 3D diagrams of the apparent molar volume (V _? ) of MgB₄O₇(aq) against temperature (T) and molality (m) were plotted. On the basis of the Vogel–Tamman–Fulcher equation, the coefficients of the correlation equation for densities of MgB₄O₇(aq) against temperature and molality were parameterized. According to the Pitzer ion-interaction model of the apparent molar volume, the temperature correlation equations of Pitzer single-salt parameters F(i,p,T)?=?a₀?+?a₁?×?T?+?a₂?×?T ²?+?a₃/T?+?a₄?×?ln(T)?+?a₅?×?T ³ (where T is temperature in Kelvin, a _i are model parameters) for MgB₄O₇ were obtained for the first time.