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Efficient and accurate calculations of stability bounds in Hamiltonian systems
No full textThe stability of motion in a typical Hamiltonian system with two degrees of freedom is described by the corresponding fractal diagram and the corresponding critical function. We extend the method of modular smoothing on the fractal diagram by showing that it possesses the same transformation properties as the critical function. This enables one to calculate the fractal diagram at all points and the critical function knowing only a few periodic orbits with the smallest periods
Singularity spectrum of a fractal diagram for a Hamiltonian system
No full textWe determine numerically the relevant f(alpha) spectrum of scaling indices for the fractal diagram of the standard map. Infinite partitions, related by the Gauss transformation and an appropriate measure had to be used in order to obtain convergent results. This choice of the measure and the partitions is motivated by the method of modular smoothing
Characterization of metal iodide quantum dots
No full textDifferent synthetic procedures for preparation of the nanometer scale metal iodide particles in liquid solutions and their incorporation in silicate glasses have been developed. Optical properties of small metal iodide particles that exhibit quantization effect has been examined. These particles are called quantum dots. Injection of electrons into semiconductor quantum dots colloids was studied by the pulse radiolysis technique. Excess electrons trapped on the surface lead to a blue-shift in the absorption edge of colloids. The change of crystal structure during the early stages of particle growth was followed by transmission electron diffraction and X-ray diffraction analysis
Characterization of the contact between TiO2 and PbS quantum dots
No full textThe synthetic procedure of the growth of one semiconductor material (PbS) on a seed of another (TiO2) have been developed. The contact between TiO2 and PbS quantum dots was characterized by optical absorption and fluorescence. The dramatic increase of the bandgap of PbS (ΔEg=1.5 eV) was observed after precipitation of PbS in the colloidal solution of TiO2. The positions of the lowest empty energy level of TiO2 and PbS single quantum dots as well as TiO2-PbS composite were determined by pulse radiolysis technique. The contact between TiO2 and PbS quantum dots leads to the transfer of electrons from PbS to TiO2
Polarographic and electrochemical studies of some aromatic and heterocyclic nitro compounds, part IV: Polarographic reduction of 2‐alkylnitroimidazoles and aminonitroimidazoles
No full text1, 2‐Dialkyl‐4‐nitroimidazoles are reduced between pH 0 and 13 in a four‐electron wave. The resulting arylhydroxylamine is stable and in acidic media reduced further to the amine. 1,2‐Dialkyl‐5‐nitroimidazoles and 2‐alkyl‐4(5)‐nitroimidazoles are reduced in alkaline media with the number of electrons approaching six. The hydroxylamine derivative formed in these reductions can be dehydrated and yields an easily reducible, quinone‐like ketimine. The rate of the dehydration governs the heights of the first step and is base catalyzed. The sequence of electron and proton transfers for 2‐ alkylsubstituted nitroimidazoles is the same as that observed for corresponding desalkyl compounds. 1‐Alkyl‐4‐amino‐5‐nitroimidazoles, as well as 1‐alkyl‐4‐nitro‐5‐aminoimidazoles, are reduced in a single wave, the height of which approaches that of a six‐electron process. The dehydration of the hydroxylamino derivative is favored, probably due to an internal base catalysis. The shifts of half‐wave potentials with pH differ principally from those of all other nitroimidazoles and indicate the predominant role of the amino group in the proton transfer
Polarographic and electrochemical studies of some aromatic and heterocyclic nitro compounds, part III: Electroreduction of mono‐ and dinitropyrazoles and ‐imidazoles
No full textThe reduction of mono‐ and dinitropyrazoles and of nitroimidazoles follows the general pattern of reduction of aromatic nitro compounds: The nitro group is reduced in a four‐electron step to a hydroxylamino group and the protonated form of the hydroxylamino group is—in the lower pH range—further reduced to an amine. This reduction differs from that of nitrobenzenes in participation of a second hydrogen ion probably involved in protonation of the heterocyclic ring. This second proton is for nitroimidazoles transferred before the uptake of the first electron, for nitropyrazoles probably after this uptake. The transfer of the second electron is indicated to be the potential determining step. The two sequences are H+, H+, e, H+, e, 2e, H+ and H+, e, H+, H+, e, 2e, H+, respectively. For nitropyrazoles and nitroimidazoles without an alkyl substituent on the ring nitrogen, the reduction process is further complicated by the dissociation of the NH‐group in the heterocyclic ring. For 1‐alkyl‐5‐nitroimidazoles, for 4(5)‐nitroimidazole and for N‐unsubstituted‐4‐ and 3(5)‐ nitropyrazoles (but not for 2‐nitroimidazoles, 1‐alkyl‐4‐nitroimidazoles and 1‐alkylnitropyrazoles) the hydroxylamino derivative formed in the first four‐electron step undergoes a base catalyzed dehydration yielding a quinone‐like ketimine. Easy reduction of this species results in alkaline solutions in a limiting current which is significantly higher than corresponds to a four‐electron and limits to a six‐electron reduction. Such dehydration reactions occur considerably faster for dihydroxylamino derivatives formed in the reduction of dinitropyrazoles resulting in two waves with total transfer of up to 12 electrons
Reactions of Hydrous Titanium Oxide Colloids with Strong Oxidizing Agents
No full textThe absorption spectra of the transients formed in the reactions of titanium hydrous oxide with SO4•-, Tl2+, or OH* species in alkaline aqueous solution have been studied by using the pulse radiolysis technique. Direct hole capture via interfacial electron transfer from colloidal titanium hydrous oxide to SO4•- radicals leads to the formation of a product which has the broad absorption spectrum with an onset at about 480 nm rising steeply toward the UV region. A completely different absorption spectrum was found for the hydroxyl radical adduct formed by the reaction of OH* with titanium hydrous oxide that has a maximum at 620 nm. This maximum disappears in acidic solution at pH 3 with assistance of H+aq which transforms the OH adduct to the product the same as that formed in the reaction with SO4•-. The low-weight aggregates of titanium hydroxide also react with OH* radicals, and in the alkaline solution a similar transient spectrum with a maximum at 570 nm was obtained. In neutral and alkaline solutions the absorption spectra of transients formed in the reactions of OH*, Tl2+, or SO4•- with TiO2 do not appear to be dependent upon the mode of the colloid preparation. However, decay kinetics of these transients are very sensitive to surface chemistry
Polarographic and electrochemical studies of some aromatic and heterocyclic nitro compounds, part II: Polarographic and voltammetric reduction of some nitramines, pyrazolium, and imidazolium nitro derivatives
No full textReduction of 1‐nitropyrazole (I) results in acidic media in a cleavage of the NN bond and formation of nitrous acid which is further reduced at more negative potentials. At pH > 4 a competitive reduction of the nitramine to nitrosamine occurs. Four‐electron reduction of nitro derivatives of pyrazolium (II) and (III) and imidazolium (IV) and (V) salts results in a formation of a hydroxylamine derivative. The reduction follows the scheme: H+, e, e, H+, 2e, 2H+. In the reduction product the azolium ring is reduced at more negative potentials. Whereas the effect of pyrazolium and imidazolium rings on the reducibility of the nitro group is comparable, the interaction between the nitro group and the azolium ring markedly depends on the position of the nitro group on the ring