On the distribution of square-full and cube-full numbers

There are many results on the distribution of square-full and cube-full numbers. In this article the distribution of these numbers are studied in more detail. Suchk-full numbers (k=2,3) are considered which are at the same time 1-free (1k+2). At first an asymptotic result is given for the numberN _k,1(x) ofk-full and 1-free numbers not exceedingx. Then the distribution of these numbers in short intervals is investigated. We obtain different estimations of the differenceN _k,1(x+h)–N_k,1(x) in the casesk=2, 1=4,5,6,7,18 andk=3, 1=5,6,7, 18.     

Generalization of an aging model

Here we present generalizations of a recently proposed aging model to include several ages and the Dauer state. The results show that increasing the number of ages does not matter in one version of the model, but matters in another version, and that the Dauer state does provide a favorable mechanism for survival.     

Rationale for kinetic heterogeneity of ultrafast light-induced electron transfer from Ru(II) complex sensitizers to nanocrystalline TiO2

Because of their successful use in dye-sensitized solar cells, Ru(II) polypyridyl complex dyes adsorbed on nanocrystalline TiO2 films have been regarded as model systems for the experimental study of the ultrafast dynamics of interfacial light-induced electron transfer. Most studies have reported charge injection kinetics from Ru(dcbpyH2)2(NCS)2 (N3) to take place with a fast (sub-100 fs) phase, followed by a slower (0.7-100 ps) multiexponential component. This complex, multiphasic behavior observed for the electron injection process has prevented the development of a satisfying kinetic model and has led to often contradicting conclusions. Here, we show that the observed kinetic heterogeneity can result from the aggregation of sensitizer molecules on the surface. Carefully controlled deposition of Ru(II) complex dye molecules onto nanocrystalline titania consistently yields a monophasic injection dynamics with a time constant shorter than 20 fs. The latter figure suggests the process is beyond the scope of vibration-mediated electron transfer kinetic models and might be controlled by the electron dephasing in the solid.     

Charakterisierung und katalytische Aktivität von Ni2+-ausgetauschten X- und Y-Zeolithen. I. TPR-Untersuchungen an NiNaX- und NiNaY-Zeolithen

Charaterization and Catalytic Activity of Ni²⁺ Exchanged X and Y Zeolites. I. TPR Studies on NiNaX and NiNaY Zeolites . The structure of TPR spectra of NiNaX and NaNiY zeolites variously exchanged is determined by the location of the cations. In case of X zeolites a peak appears with a maximum at 750–800 K (reduction on S_II and S_I, positions) and for higher exchange degrees an additional one at about 1000 K (reduction on S_I positions). Three ranges of reduction may be separated in case of Y zeolites (reduction on S_II, S_I′, and S_I). With increasing Si/Al ratios the maximum of the hightemperature peak is shifted to higher temperatures. The reduction at temperatures up to 800 K resulted in higher reduction degrees for X reolites while the overall reduction up to high temperatures led to higher reduction degrees for Y zeolites. The kinetic analysis by means of two different methods yielded the following activation energies: (85 ± 10) or (86 ± 2) kJ/mole, respectively, for the low-temperature peak, and (223 ± 12) or (214 ± 2) kJ/mole, respectively, for the high-temperature peak.     

Molecular control of recombination dynamics in dye-sensitized nanocrystalline TiO2 films: free energy vs distance dependence

In this paper we address the dependence of the charge recombination dynamics in dye-sensitized, nanocrystalline TiO2 films upon the properties of the sensitizer dye employed. In particular we focus upon dependence of the charge recombination kinetics upon the dye oxidation potential E0(D+/D), determined electrochemically, and the spatial separation r of the dye cation HOMO orbital from the metal oxide surface, determined by semiempirical calculations. Our studies employed a series of ruthenium bipyridyl dyes in addition to porphyrin and phthalocyanine dyes. A strong correlation is observed between the recombination dynamics and the spatial separation r, with variation in r by 3 A resulting in a more than 10-fold change in the recombination half-time t(50%). This correlation is found to be in agreement with electron tunneling theory, t(50%) proportional, variant exp(-betar) with beta = 0.95 +/- 0.2 A-1. In contrast, the recombination dynamics were found to be relatively insensitive to variations in E0D+/D), indicative of the recombination reaction lying near the peak of the Marcus free energy curve, DeltaG approximately lambda, and with lambda approximately 0.8 eV. A correlation is also observed between the recombination half-time and the temporal shape of the kinetics, with faster recombination dynamics being more dispersive (less monoexponential). Comparison with numerical Monte Carlo type simulations suggests this correlation is attributed to a shift from fast recombination dynamics primarily limited by dispersive electron transport within the metal oxide film to slower dynamics primarily limited by the interfacial electron-transfer reaction. We conclude that the primary factor controlling the charge recombination dynamics in dye-sensitized, nanocrystalline TiO2 films is the spatial separation of the dye cation from the electrode surface. In particular, we show that for the Ru(dcbpy)2NCS2 dye series, the use of X = NCS rather than X = CN results in a 2 A shift in the dye cation HOMO orbital away from the electrode surface, causing a 7-fold retardation of the recombination dynamics, resulting in the remarkably slow recombination dynamics observed for this sensitizer dye.     

Integrated Systems for Water Cleavage by Visible Light; Sensitization of TiO2 Particles by Surface Derivatization with Ruthenium Complexes

Irradiation of acidic (pH 2) solutions of RuL₃²⁺ 2Cl^? (L = diisopropyl 2,2′-bipyridine-4,4′ -dicarboxylate) in the presence of TiO₂ at 100°C leads to the loss of one bipyridyl ligand and the chemical fixation of RuL₂ at the surface of teh TiO₂ particles through formation of Ru-O-Ti bonds. These surface complexes are very stable and shift the absorption onset of TiO₂ beyond 600 mm. Efficient sensitization H₂-generation is achieved with this system beginning in the wave length domain between 590 and 665 nm. Preliminary water cleavage experiments with bifunctional TiO₂/Pt/RuO₂ redox catalyst are reported.     

Mixed‐Organic‐Cation Perovskite Photovoltaics for Enhanced Solar‐Light Harvesting

Hybrid organic–inorganic lead halide perovskite APbX₃ pigments, such as methylammonium lead iodide, have recently emerged as excellent light harvesters in solid‐state mesoscopic solar cells. An important target for the further improvement of the performance of perovskite‐based photovoltaics is to extend their optical‐absorption onset further into the red to enhance solar‐light harvesting. Herein, we show that this goal can be reached by using a mixture of formamidinium (HN=CHNH₃⁺, FA) and methylammonium (CH₃NH₃⁺, MA) cations in the A position of the APbI₃ perovskite structure. This combination leads to an enhanced short‐circuit current and thus superior devices to those based on only CH₃NH₃⁺. This concept has not been applied previously in perovskite‐based solar cells. It shows great potential as a versatile tool to tune the structural, electrical, and optoelectronic properties of the light‐harvesting materials.