Hamiltonian walks on Sierpinski and n-simplex fractals

We study Hamiltonian walks (HWs) on Sierpinski and $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ and find the asymptotic behaviour of the number of HWs. Depending on whether or not the polymer collapse transition is possible on a studied lattice, different scaling relations for the number of HWs are obtained. These relations are in general different from the well-known form characteristic of homogeneous lattices which has thus far been assumed to hold for fractal lattices too.Comment: 22 pages, 6 figures; final versio

Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure

Reakcija redukcije kiseonika na elektrohemijski istaloženim tankim slojevima platine na (Nb-Ti)2alc nosaču

Catalytic activity towards the oxygen reduction reaction (ORR) in 0.5 M H2SO4 was investigated at sub-monolayers and ultra-thin layers (corresponding to 10, 30 and 100 monolayers, (MLs)) of Pt electrochemically deposited on (Nb-Ti)2AlC substrate. Electrochemical deposition of Pt layers on (Nb-Ti)2AlC substrate was achieved from the solution containing 3 mM K2PtCl4 + 0.5 M NaCl (pH 4) under the conditions of convective diffusion (RPM = 400) using linear sweep voltammetry (LSV) at a sweep rate of 2 mV s-1, by determining limiting potential for deposition of each Pt sample from the QPt vs. E curves. The Pt samples were characterized X-ray photoelectron spectroscopy (XPS). XPS analysis showed that practically the whole surface of (Nb-Ti)2AlC substrate is covered with homogeneous layer of Pt, while Pt ion reduction was complete to metallic form – Pt(0) valence state. Then oxygen reduction was studied at rotating disc electrode by cyclic voltammetry and linear sweep voltammetry. Two different Tafel slopes were observed, one close to 60 mV dec-1 in low current densities region and second one ~ 120 mV dec-1 in high current densities region. This novel catalyst exhibited higher activity in comparison to carbon supported one, in terms of mass activity – kinetic current density normalized to Pt loading

Ru–Co alloy coatings electrodeposited on a MAX phase substrate as efficient catalysts for the hydrogen evolution reaction

This study investigates the structure, electrochemical behavior and hydrogen evolution reaction (HER) performance of electrodeposited Ru–Co alloy coatings. The alloys were prepared from a 0.75 M Co2+ + 0.025 M Ru3+ solution at various potentials ranging from −0.5 to −1.2 V vs. SCE. Results reveal that the Ru and Co deposition processes are interdependent. The deposition of nobler Ru from the mixed metal solution reaches pure diffusion control already at −0.7 V compared to −1.0 V from a single Ru bath. On the other hand, Co deposition is significantly facilitated in the presence of Ru in the solution. Consequently, as the deposition potential changes from −0.6 to −1.0 V, Ru–Co solid solution coatings characterized by a distinct globular morphology are formed, with their Co content increasing from 22.1/7.4 to 70.2/86.1 wt% for the Cu/Ti2AlC MAX phase substrate applied. The alloy catalysts are found to show much better HER activity and stability in alkaline than in acidic solutions. The best Ru–Co@Ti2AlC sample, electrodeposited at −0.6 V, requires an overpotential of only −95 mV to deliver a current density of −100 mA cm−2 in 1 M KOH, thus outperforming most Ru–Co-based HER electrocatalysts reported to date

Fe-Mo alloy coatings as cathodes in chlorate production process

The aim of this study was to gain a better understanding of the feasibility of partial replacement of dichromate, Cr(VI), with phosphate buffer, focusing on the cathode reaction selectivity for hydrogen evolution on mild steel and Fe-Mo cathodes in undivided cell for chlorate production. To evaluate the ability of phosphate and Cr(VI) additions to hinder hypochlorite and chlorate reduction, overall current efficiency (CE) measurements in laboratory cell for chlorate production on stationary electrodes were performed. The concentration of hypochlorite was determined by a conventional potentiometric titration method using 0.01 mol dm-3 As2O3 solution as a titrant. The chlorate concentration was determined by excess of 1.0 mol dm-3 As2O3 solution and excess of arsenic oxide was titrated with 0.1 mol dm-3 KBrO3 solution in a strong acidic solution. Cathodic hypochlorite and chlorate reduction were suppressed efficiently by addition of 3 g dm-3 dichromate at both cathodes, except that Fe-Mo cathode exhibited higher catalytic activity for hydrogen evolution reaction (HER). The overvoltage for the HER was around 0.17 V lower on Fe-Mo cathode than on mild steel at the current density of 3 kA m-2. It was found that a dichromate content as low as 0.1 g dm-3 is sufficient for complete suppression of cathodic hypochlorite and chlorate reduction onto Fe-Mo catalyst in phosphate buffering system (3 g dm-3 Na2HPO4 + NaH2PO4). The overall current efficiency was practically the same as in the case of the presence of 3 g dm-3 dichromate buffer (98 %). However, for the mild steel cathode, the overall current efficiency for the chlorate production was somewhat lower in the above mentioned mixed phosphate + dichromate buffering system (95%) than in the pure dichromate buffering solution (97.5%)