Search

The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker–Doring-type equation). The transition to a continuum description is performed.

The electrochemical behavior of phthaloyl peroxide C8H4O4 on an Au disk electrode in a 0.05 M aqueous solution of Na2SO4 was studied by cyclic voltammetry (CVA). It demonstrated a high activity in cathodic reduction with the formation of an irreversible peak on the CVA curve at E =–0.81 V. Additionally, during the anodic oxidation of C8H4O4, the surface of the Au electrode became passivated by compounds which prevented its oxidation during the registration of repeated cycles. Apparently, these compounds are surface complexes of phthaloyl peroxide with a gold cation.

In this paper the generalizations of the physico-chemical kinetics equations, including classical and quantum physico-chemical kinetics, coagulation–fragmentation equations, discrete velocity models of classical and quantum kinetic equation and, generally speaking, all discrete physico-chemical kinetics is considered. We make time discrete in these equations and prove the H -theorem.

The adsorption of 2,4-dichlorophenoxyacetic acid (2,4-D) as a typical herbicide from aqueous solutions on activated carbons prepared based on polyvinyl chloride by its alkaline dehydrochlorination and the subsequent heat treatment was studied. The structure of the activated carbon surface and the presence of functional groups on it were established. The kinetics of the process of adsorption was studied. The influence of activated carbon preparation conditions on the properties of the adsorbents was demonstrated.

The birefringence of the new Ba 2 Na 3 [B 3 O 6 ] 2 F (BNBF) ( P 6 3 / m ) and Ba 7 (BO 3 ) 4 −y F 2+3 y ( P 6 3 ) phases has been investigated. Coefficients of the Sellmeier equations have been determined. Parallel [B 3 O 6 ] 3− rings in the Ba 2 Na 3 [B 3 O 6 ] 2 F structure generate the major anisotropic polarizabilities and produce large birefringence Δ n = 0.1097 − 0.0428 from 350 nm to 5 μm, comparable to that of commercial birefringent crystal α-BaB 2 O 4 . A new flux for growing a high quality BNBF crystal has been proposed. In the measured wavelength range from 266 nm to 1.7 μm noncentrosymmetric phase Ba 7 (BO 3 ) 4 −y F 2+3 y (y = 0.49) exhibits low birefringence Δ n = 0.0111 − 0.0037 which can be accounted for non-coplanar arrangement of the anionic groups in the structure. Low birefringence prevents the use of this crystal for nonlinear optical applications, since phase-matching conditions for second harmonic generation can not be reached.

The kinetics of adsorption of 2,4-dichlorophenoxyacetic acid (2,4-D) as a typical herbicide from aqueous solutions on coconut shell activated carbon was studied without preliminary treatment. The surface structure of the activated carbon, which is responsible for its properties, was characterized. The order of reaction in the process of adsorption was determined. The high adsorption capacity of the coconut shell activated carbon was shown.

The kinetics of adsorption of ethyl benzoate from solutions in ethanol on coconut shell activated carbon was studied. It was found that the kinetics of adsorption of ethyl benzoate can be described by pseudofirst-order and pseudo-second-order rate equations with the same accuracy. It was established that the adsorption isotherm at a concentration to 2 g/L in the initial solution is adequately described by the Langmuir equation.

New kinetic equations are proposed from which the incompressible Euler and Navier–Stokes equations are derived by making an exact substitution. A class of exact solutions of the Navier–Stokes equation and the form of singularities for a gradient catastrophe are obtained.

It is well known that the Schrodinger equation can be reduced to the Hamilton–Jacobi equation in Bohmian mechanics. Corresponding new equations of the Vlasov and Lamb types are derived, and their stationary solutions are investigated.

The anodic corrosion of gold followed by its deposition on the cathode as a compact precipitate occurs upon electrolysis of weakly alkaline aqueous solutions of diaminoalkanes, among which 1,2-diaminoethane proved to be the most effective. The process has been characterized by cyclic voltammetry.

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann&rsquo, s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation&ndash, fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.

This paper reports on new experimental results on the temperature-dependent phase-matching properties of LiGaS

The corrosion of a Au anode in a solution of 1,3-diaminopropane (DAP) is studied by means of gravimetry. It is found that the products of corrosion of Au electrode in galvanostatic conditions are reduced on a Pt cathode with the formation of either an electrolytic Au deposit or a colloidal solution of metallic Au, depending on the current strength. The kinetics of the dissolution of Au in the presence of DAP is investigated. The formation of a complex of Au with DAP is observed, and a structure for it is proposed.

The kinetics of adsorption of benzoyl peroxide from solutions in ethanol and n-hexane on coconut shell activated carbon was studied. It was found that the kinetics of adsorption of benzoyl peroxide is described by a pseudo-first-order rate equation. The adsorption isotherm of benzoyl peroxide at its equilibrium concentrations from 0.07 to 1.25 g/L in solution is adequately described by the Langmuir equation. It was established that, in a solution in ethyl alcohol, the degradation of benzoyl peroxide with the formation of ethyl benzoate occurred along with adsorption.

The electrochemical corrosion of gold in solutions of 6,6-dimethyl-1,5-diazabicyclo[3.1.0]hexane (I) and 6-methyl-1,5-diazabicyclo[3.1.0]hexane (II) on a gold electrode is studied via cyclic voltammetry. It is shown that the galvanostatic electrolysis of weakly basic aqueous solutions of I and II on gold anodes results in the corrosion of Au electrodes, probably with the formation of organic complexes of gold that are reduced to form a gold mirror on the inner surface of an electrochemical cell during electrolysis. A mechanism is proposed for the investigated processes.

Kinetics of N-chloromethylamine decomposition in an aqueous base medium and chloroform at different temperatures is studied. The decomposition of N-chloromethylamine is found to obey a second order equation in an aqueous base medium at an equimolar ratio of the reagents and a first order equation in chloroform with excess base. The activation energy of N-chloromethylamine decomposition in the both solvents is determined. A mechanism for the reaction is proposed. N-Chloromethylamine is shown to have approximately equal stability in these solvents within the studied temperature range.

The behavior of [1,2-bis(tert-butylperoxy)ethyl]benzene (I) on Pt electrode is studied by means of cyclic voltammetry (CVA). A comparison of the electrochemical properties of I and the properties of previously studied bridge-type 1,2,4,5-tetraoxane ((1,4)-1,4-dimethyl-7-(4-methylbenzyl)-2,3,5,6-tetraoxabicyclo[2.2.1]heptane) (II) shows that the biperoxide studied in this work is reduced on a Pt electrode at lower cathodic potentials and is resistant to electrooxidation.

The kinetics and thermodynamics of the adsorption of diclofenac sodium from aqueous solutions of different concentrations at different temperatures on activated carbon obtained from coconut shell were studied. It was found that the adsorption of diclofenac sodium is described by a pseudo-first-order equation and the adsorption isotherm at its concentration to 750 mg/L in the initial solution is adequately described by the Langmuir equation. It was found that the adsorption of diclofenac sodium is an endothermic process.

Rippite K2(Nb,Ti)2(Si4O12)(O,F)2, a new K-Nb-cyclosilicate, has been discovered in calciocarbonatites from the Chuktukon massif (Chadobets upland, SW Siberian Platform, Krasnoyarsk Territory, Russia). It was found in a primary mineral assemblage, which also includes calcite, fluorcalciopyrochlore, tainiolite, fluorapatite, fluorite, Nb-rich rutile, olekminskite, K-feldspar, Fe-Mn&ndash, dolomite and quartz. Goethite, francolite (Sr-rich carbonate&ndash, fluorapatite) and psilomelane (roman&egrave, chite &plusmn, hollandite) aggregates as well as barite, monazite-(Ce), parisite-(Ce), synchysite-(Ce) and Sr-Ba-Pb-rich keno-/hydropyrochlore are related to a stage of metasomatic (hydrothermal) alteration of carbonatites. The calcite&ndash, dolomite coexistence assumes crystallization temperature near 837 &deg, C for the primary carbonatite paragenesis. Rippite is tetragonal: P4bm, a = 8.73885(16), c = 8.1277(2) &Aring, V = 620.69(2) &Aring, 3, Z = 2. It is closely identical in the structure and cell parameters to synthetic K2Nb2(Si4O12)O2 (or KNbSi2O7). Similar to synthetic phase, the mineral has nonlinear properties. Some optical and physical properties for rippite are: colorless, Mohs&rsquo, hardness&mdash, 4&ndash, 5, cleavage&mdash, (001) very perfect, (100) perfect to distinct, density (meas.)&mdash, 3.17(2) g/cm3, density (calc.)&mdash, 3.198 g/cm3, optically uniaxial (+), &omega, = 1.737-1.739, &epsilon, = 1.747 (589 nm). The empirical formula of the holotype rippite (mean of 120 analyses) is K2(Nb1.90Ti0.09Zr0.01)[Si4O12](O1.78OH0.12F0.10). Majority of rippite prismatic crystals are weakly zoned and show Ti-poor composition K2(Nb1.93Ti0.05Zr0.02)[Si4O12](O1.93F0.07). Raman and IR spectroscopy, and SIMS data indicate very low H2O content (0.09&ndash, 0.23 wt %). Some grains may contain an outermost zone, which is enriched in Ti (+Zr) and F, up to K2(Nb1.67Ti0.32Zr0.01)[Si4O12](O1.67F0.33). It strongly suggests the incorporation of (Ti,Zr) and F in the structure of rippite via the isomorphism Nb5+ + O2&minus, &rarr, (Ti,Zr)4+ + F1&minus, The content of a hypothetical end-member K2Ti2[Si4O12]F2 may be up to 17 mol. %. Rippite represents a new structural type among [Si4O12]-cyclosilicates because of specific type of connection of the octahedral chains and [Si4O12]8&minus, rings. In structural and chemical aspects it seems to be in close with the labuntsovite-supergroup minerals, namely with vuoriyarvite-(K), K2(Nb,Ti)2(Si4O12)(O,OH)2∙4H2O.

In the present paper we make the transition from the Becker–Doring system of equations to the hybrid (discrete and continuum) description. This new type of system of equations consists of the equation of the Fokker–Planck–Einstein–Kolmogorov type added by the Becker–Doring equations. We consider the H -theorem for it. We also consider the H -theorem for the Becker–Doring system of equations with discrete time and showed that it is true for some partially implicit discretization in time. Due to generality of the kinetic approach the present work can be useful for specialists in different spheres engaged in modeling the evolution of structures differing by properties.

A comparative study of picosecond mid-IR difference frequency generation in a wide wavelength range of 4.6-10.8 µm in a simple down-converter based on the 8-mm long, high-damage-threshold crystals of LiGaS2 or LiGaSe2 under the 5-mJ, 20-ps, 1.064-µm Nd:YAG laser pumping and the single-pass crystalline (CaCO3, BaWO4, CVD-diamond) Raman laser seeding was presented. 10-µJ-level, narrowband (−1) generation at discrete wavelengths of 4.6, 5.4, 7.5, and 9.2 µm with the optical frequencies equal to the vibrational Raman frequency or its second harmonic of various crystalline Raman seeders was demonstrated. Optimization of the pump spot and mode-matching between the pump and signal spots allowed to increase the output pulse energy up to 50 µJ in the case of LiGaSe2.

We considered derivation of Vlasov–Einstein–Maxwell system of equations from the first principles, i.e. using classical Maxwell–Einstein–Hilbert action principle. We know many papers in which the theories indicated as Einstein–Vlasov, Vlasov–Maxwell–Einstein, Einstein–Maxwell–Boltzmann are discussed, and we discuss difficulties of usually used equations. We use another way of derivation and obtain an alternative version based on the generalized Fock–Weinberg form of equation of motion.