Elena Zhizhina

Nonequilibrium Glauber-type dynamics in continuum

We construct the nonequilibrium Glauber dynamics as a Markov process in configuration space for an infinite particle system in continuum with a general class of initial distributions. This class we define in terms of correlation functions bounds and it is preserved during the Markov evolution we constructed.

ONE-PARTICLE SUBSPACE OF THE GLAUBER DYNAMICS GENERATOR FOR CONTINUOUS PARTICLE SYSTEMS

We consider a Glauber-type stochastic dynamics of continuous particle systems in ℝd. We construct a one-particle invariant subspace of the generator of this dynamics in the high temperature and low density regime. We prove that under some additional assumptions on the decay of the potential the restriction of the generator on the one-particle subspace is unitary equivalent to the operator of the multiplication by a bounded smooth real-valued function. As a consequence we estimate the spectral gap of the generator and find the second gap between the one-particle branch and the rest of the spectrum.

Catalytic oxidation of organic compounds with oxygen in the presence of Mo-V-phosphoric heteropoly acid solutions

The studies carried out at the Institute of Catalysis, Siberian Branch, Russian Academy of Sciences, on the selective catalytic oxidation of organic compounds with oxygen in the presence of aqueous solutions of Mo-V-phosphoric heteropoly acids (HPAs) are reviewed. Alkylphenols are oxidized into 1,4-quinones with a selectivity of 85–99%, and C2-C4 olefins in the presence of Pd complexes are oxidized into carbonyl compounds with a selectivity of 98–99%. The bifunctional (acidic and oxidizing) properties of HPA solutions were used for the first time to synthesize anthraquinones and vitamin K3.

Kinetics of the oxidation of reduced Mo-V-phosphoric heteropoly acid species with dioxygen in concentrated aqueous solutions

Concentrated (0.2 M) aqueous solutions of HP-acids, such as H3+x+mPVIVmVVx-mMo12-xO40 and their analogues with an excess VO2+ cation, are oxidized by dioxygen at 343 K and atmospheric pressure through intermediate active complexes (IAC) [Hx+m-1PVIVmVVx-mMo12-xO404-] · [VO2+]y · O2, where m + y ≥ 3. The electron transfer to the coordinated O2 molecule inside AC is the limiting stage at high m. At low m, the formation of IAC becomes the limiting stage that results in a sharp decrease in the oxidation rate.

Aqueous Solutions of Mo‐V‐Phosphoric Heteropoly Acids as Bifunctional Catalysts For Preparation of 9,10‐Anthraquinone and its Hydrogenated Derivatives

Acid‐catalyzed condensation of 1,3‐butadiene with para‐quinones and oxidation of resulting adducts can be performed as a one‐pot process in the presence of aqueous solutions of Mo‐V‐phosphoric heteropoly acids (HPA) with the general formula HaPzMoyVxOb. These solutions have bifunctional catalytic properties; they are both strong Brønsted acids and reversible oxidants. Condensation of hydroquinone, 1,4‐benzoquinone, or 1,4‐naphthoquinone with 1,3‐butadiene in the HPA solutions results in 9,10‐anthraquinone (AQ) in a mixture with tetrahydro‐AQ (THA) and dihydro‐AQ (DHA). In this one‐pot process, which proceeds in the absence of organic solvents, the HPA solution is reduced. A slightly soluble mixture of THA, DHA, and AQ is precipitated and filtered off. The non‐Keggin‐type H12P3Mo18V7O85 solution is the most effective in this process. This solution can be rapidly regenerated by dioxygen or air at temperatures of up to 170 °C and then reused. The prepared THA+DHA+AQ mixture can be used as a catalyst for alkaline delignification of wood. Our homogeneous bifunctional HPA catalyst is very stable and promising for use in similar one‐pot processes.

Thermochemical Study of Reduction and Oxidation Reactions of Molybdovanadophosphoric Heteropolyacids in Aqueous Solutions

Differential enthalpies of reduction, –ΔrH4j, have been found at 343 K for 0.2 m aqueous heteropolyacids H3+xPVxMo12–xO40 (HPA-x, where 1 ≤ x ≤ 6) and their salts by hydrazine hydrate (HH). The –ΔrH4j values depend on x and m, where m = [VIV]/[HPA-x]. At m ≈ 0, the initial –ΔrH4j value is 436 ± 14 kJ mol−1 HH for all HPA-x. For HPA-x with 3 ≤ x ≤ 6, the curves –ΔrH4j = f(mj) have maxima associated with formation and reduction of the outer-sphere cation VVVIVO33+. A similar maximum is observed on reduction of 0.1 M VO2ClO4 in 4 M HClO4. No maxima are observed for the reduction of HPA-1, HPA-2, and salts of HPA-3. For HPA-3 salts, –ΔrH4j = f(mj) depends primarily on the pH of the salt solution, rather than on the nature of the cation. Reduction and oxidation of HPA-x and their salts are reversible reactions. In HPA-x solutions, VO2+ in the outer sphere is reduced first, and VV in the inner coordination sphere of the heteropoly anion is reduced next. Differential enthalpies for the oxidation of the reduced HPA-x by dioxygen (–ΔrH2j) have been calculated. The sequence of the oxidation of different VIV forms in the reduced HmHPA-x solutions is the reverse of that for the reduction of the VV forms in the initial HPA-x solutions.

Kinetics of oxidation of butene-1 to butanone in aqueous solution in the presence of ions Pd2+ and Mo-V-phosphoric heteropoly acid

Oxidation of butene-1 to butanone in the presence of homogeneous catalysts (PdSO4 + HPA-x), where HPA-x = H3+xPVxMo12-xO40, 1 £ x £ 4, was investigated. This reaction is found to be of the 1st order with respect to C4H8, and of the 0.64th order with respect to Pd. The reaction rate does not depend on the HPA-x concentration and pH of the solution. The activation energy of the reaction is variable. A kinetic expression of the reaction is obtained for 303-343 K.

On an aggregation in birth-and-death stochastic dynamics

We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.

New catalytic method for the synthesis of vitamins K

A new catalytic method for the synthesis of vitamins of the K family is suggested. In this method 2-methyl-1-naphthol is oxidized by dioxygen in the presence of Mo-V-P heteropoly acids or their salts in a two-phase system (organic solvent + water) to 2-methyl-1,4-naphthoquinone or vitamin K3, which is the precursor of all K family vitamins.

Phase-transfer oxidation of 2-methyl-1-naphthol into 2-methyl-1,4-naphthoquinone in the presence of vanadomolybdophosphoric heteropolyacids

Abstract2-Methyl-1-naphthol is oxidized into 2-methyl-1,4-naphthoquinone (menadione) by air in the presence of vanadomolybdophosphoric heteropolyacids and their salts. The reaction proceeds in a biphasic system, and the yield of menadione is up to 85 %. The influence of the composition of the heteropolyacids on the rate and the selectivity of the reaction was studied, and the reaction mechanism was proposed.