Critical phenomena in ethylbenzene oxidation in acetic acid solution at high cobalt(<Emphasis Type="SmallCaps">II</Emphasis>) concentrations

Critical phenomena in ethylbenzene oxidation in an acetic acid solution at high cobalt(III) concentrations (from 0.01 to 0.2 mol L⁻¹) were studied at 60–90 °C by the gasometric (O₂ absorption), spectrophotometric (Co^III accumulation), and chemiluminescence (relative concentration of radical RO₂ ^·) methods. These phenomena are as follows: (1) increase in the oxidation rate above the theoretical limiting rate of radical autooxidation (k ₃ ²[RH]²/2k ₆); (2) achievement of a maximum and a sharp decrease in the oxidation rate and concentration of radical RO₂ ^· with the further increase in the Co^II concentration (existence of critical concentrations). The oxidation rate increases due to the reaction RO₂ ^· + Co^II + H⁺ → → ROOH + Co^III, while the inhibition effect is caused by the decay of RO₂ ^· radical involving two cobalt(II) atoms: RO₂ ^· + 2 Co^II → R′CO + Co^III + Co^II (k(70 °C) ≈ 300 L² mol⁻² s⁻¹). The detailed scheme (through the formation of the complex RO₂ ^·Co^II) describing the conjugation of these reactions was proposed. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1823–1827, August, 2005.     

Cellular automata and statistical mechanical models

We elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel,probabilistic systems whose computational abilities rely on the cooperative behavior of their components.On leave from Institute for Theoretical Physics, Roland Eötvös University, Budapest, Hungary.     

Study of the required HLB for the solubilization of cholesterol in aqueous solution

 The solubilization of cholesterol by anionic surfactant mixtures was studied as a function of their HLB values. The relationship between the logarithm of the critical micelle concentration and the HLB value of the mixtures was not linear, which was attributed to a lack of strict additivity of the HLB values. The solubilized cholesterol/surfactant ratio was determined and it was found to be higher than that in bile salts in all the studied surfactant mixtures. Below HLB=24, emulsions were obtained, and the remaining cholesterol was solid. Above that value, limpid solutions were obtained, giving a solubility maximum at HLB≈35. The non-solubilized cholesterol was mainly in the form of lamellar mesophase. Received: 23 June 1997 Accepted: 12 August 1997     

Phase transition in swollen gels 31. Swelling and mechanical behaviour of interpenetrating networks composed of poly(1-vinyl-2-pyrrolidone) and polyacrylamide in water/acetone mixtures

Swelling and mechanical behaviour of interpenetrating positively charged polymer networks (IPNs), composed of poly(1-vinyl-2-pyrrolidone) (PVP) networks and polyacrylamide (PAAm) networks, was investigated in water/acetone mixtures. The first PVP networks were prepared by radiation polymerization at room temperature; after that the PVP networks were swollen in PAAm aqueous solutions and the networks were prepared by thermal copolymerization at 65 °C. The IPNs were prepared with various amounts of the two charged comonomers (quaternary ammonium salts) in the presence of crosslinkers. Two transition regions, detected in the dependence of swelling ratio X on acetone concentration a, suggest that a two-phase structure was formed. The first transition, located between 44 and 60 vol% of acetone, corresponds to PAAm networks, while the second transition, located at 75 vol% of acetone, corresponds to PVP networks. Depending on the amount of positive charges bound to chains, both transitions exhibit continuous or discontinuous character; this fact indicates that intermolecular interactions between the two components occur with the formation of IPNs (e.g., more polar, charged PVP component increases the extent of hydrogen bonding and makes acetone less effective solvent for IPNs at the PAAm transition). The dependences of log G on log X are roughly the same regardless of charge concentrations; this means that the mechanical behaviour is predominantly determined by the degree of swelling for all gels.     

The quantum ground state of a Heisenberg ferromagnet with an “easy-plane” type anisotropy

For the Heisenberg ferromagnet with the easy-plane type anisotropy the ground state energy and the magnetization are found with the help of perturbation theory supposing that the anisotropy energy is less than the exchange one. The study is carried out exactly without using any spin operators representation. Therefore, it is valid for a spin of any magnitude.     

Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map

The spectrum and eigenfunctions of the Frobenius-Perron operator induced by the tent map are discussed in detail. Special attention is paid to the case where the critical point of the map lies on an aperiodic trajectory and the differences from maps with a periodic critical trajectory are stressed. It is shown that the relevant eigenvalues of the spectrum are not sensitive to the aperiodicity of the critical trajectory. All other parts of the spectrum and all eigenfunctions in particular are changed drastically if the critical trajectory becomes aperiodic. The intimate connection between the point spectrum and the kneading invariant is established and the critical slowing down as well as the band splitting are a consequence of its properties. The structure of the infinite sequence of null spaces and its implications on the spectrum of the operator are discussed. It is shown that any initial distributionP(0,x) of bounded variation can be projected uniquely onto the eigenfunctions of the relevant eigenvalues and that the time dependence ofP(n, x) is determined by this expansion up to an errorO( ⁿ). From this the stationary and the asymptotic behavior of the correlation function x(n) x can be derived exactly.     

微波大功率稀土复合石榴石铁氧体的研究

报道了用稀土元素Gd,Dy和金属元素Al,Mn等按适当比例部分置换Y,Fe制备钇钆镝复合石榴石铁氧体((YGdDy)IG)的研制方案和实验结果。实验结果表明,该种材料除具有优良的旋磁特性外,还兼备承受高平均功率和高峰值功率的性能。其主要特性参数为:4πMs依实用需要可在48～96mT内选择,且具有甚高的温度稳定度:在0～160℃范围内Ms的温度系数αM≤2.8×10-4℃-1;电阻率ρ高达1013Ω·m,介电损耗tanδe≤4×10-4;居里温度TC≥500K;共振线宽ΔH=3.4～6.4kA·m-1;门阈场Hcrit适用于MW级脉冲功率。该种铁氧体可用作甚高频及微波低频段、超大功率的环行器和变极化器等微波器件。     

A generalized Sard theorem on real closed fields

We work with semi‐algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.     

Studies of Synthesis and Interfacial Properties of Sodium Branched‐Alkylbenzenesulfonates

Two sodium branched‐alkylbenzensulfonates with additional alkyl substituents were synthesized through a series of reactions. The interfacial tension of these alkylbenzenesulfonates between 1.0% NaCl solution and six n‐alkanes were measured. From the data of measurements the following values were calculated: critical micelle concentration (cmc), the interfacial tension at the cmc (γ_cmc), interfacial excess concentration at the cmc (Γ_m), area per molecule at the cmc (A_m). There were a minimum γ_cmc and a maximum Γ_m appeared for the same n‐alkane with increasing the hydrocarbon chain length of the oil. These indicated that the hydrocarbon chain length of oil have the important effect on adsorption and interfacial tension.