Visible‐Light‐Induced Photocatalytic Hydrogen Production over Binuclear RuII–Bipyridyl Dye‐Sensitized TiO2 without Noble Metal Loading

Highly efficient, visible light induced photocatalytic H₂ production was achieved over a TiO₂ system sensitized by binuclear Ru^II bipyridyl (bpy) complex [Ru₂(bpy)₄(BL)](ClO₄)₂ (BL=bridging ligand) without Pt loading, which is almost unaffected by pH in aqueous solution in the wide range from pH 5.00 to 10.50, although the dye molecules can only be loosely attached to TiO₂ due to the absence of terminal carboxyl groups. The photocatalyst shows remarkable long‐term stability and reproducibility of H₂ evolution even after exchanging the aqueous triethanolamine solution. The amount of H₂ evolved over 100 mg of photocatalyst in 27 h of irradiation corresponds to a turnover number of about 75 340, and the apparent quantum yields are estimated to be 16.8 and 7.3 % under 420 and 475 nm monochromatic light irradiation, respectively. A comparative study shows that the loosely attached dye [Ru₂(bpy)₄(BL)](ClO₄)₂ has higher photosensitization efficiency than tightly linked dyes with terminal carboxyl groups, such as [Ru₂(dcbpy)₄(BL)](ClO₄)₂ and N719. It can be rationalized by their different coordination, physicochemical, electron‐injection, and back‐transfer properties.     

Visible-Light-Induced Photocatalytic Hydrogen Production over Binuclear Ru(II) -Bipyridyl Dye-Sensitized TiO(2) without Noble Metal Loading

Highly efficient, visible light induced photocatalytic H(2) production was achieved over a TiO(2) system sensitized by binuclear Ru(II) bipyridyl (bpy) complex [Ru(2) (bpy)(4) (BL)](ClO(4) )(2) (BL=bridging ligand) without Pt loading, which is almost unaffected by pH in aqueous solution in the wide range from pH?5.00 to 10.50, although the dye molecules can only be loosely attached to TiO(2) due to the absence of terminal carboxyl groups. The photocatalyst shows remarkable long-term stability and reproducibility of H(2) evolution even after exchanging the aqueous triethanolamine solution. The amount of H(2) evolved over 100?mg of photocatalyst in 27?h of irradiation corresponds to a turnover number of about 75?340, and the apparent quantum yields are estimated to be 16.8 and 7.3?% under 420 and 475?nm monochromatic light irradiation, respectively. A comparative study shows that the loosely attached dye [Ru(2) (bpy)(4) (BL)](ClO(4) )(2) has higher photosensitization efficiency than tightly linked dyes with terminal carboxyl groups, such as [Ru(2) (dcbpy)(4) (BL)](ClO(4) )(2) and N719. It can be rationalized by their different coordination, physicochemical, electron-injection, and back-transfer properties.     

Powers of cyclotomic integers and difference sets

Let p be an odd prime, $\text{ζ =}\text{rxp}\text{(}\text{2πi}\text{p}\text{)}$, D a difference set mod p having a nontrivial multiplier, and ν = H(ζ), where H(x) is the Hall polynomial of D. For any α = Σ_i=0^p?1a_iζⁱ with rational a_i denote δ(α) = max ∥ a_i ? a_j ∥. Assuming that there are no nontrivial multiplicative dependence relations among the conjugates of ν, we obtain results for

. We then show that for most known families of difference sets mod p the required independence result is valid. A conjecture concerning the exact value of the first number is stated. The conjecture is confirmed in certain particular cases.     

Ultrafast Two‐Dimensional NMR Relaxometry for Investigating Molecular Processes in Real Time

Nuclear spin–lattice (T₁) and spin–spin (T₂) relaxation times provide versatile information about the dynamics and structure of substances, such as proteins, polymers, porous media, and so forth. Multidimensional experiments increase the information content and resolution of NMR relaxometry, but they also multiply the measurement time. To overcome this issue, we present an efficient strategy for a single‐scan measurement of a 2D T₁–T₂ correlation map. The method shortens the experimental time by one to three orders of magnitude as compared to the conventional method, offering an unprecedented opportunity to study molecular processes in real‐time. We demonstrate that, despite the tremendous speed‐up, the T₁–T₂ correlation maps determined by the single‐scan method are in good agreement with the maps measured by the conventional method. The concept of the single‐scan T₁–T₂ correlation experiment is applicable to a broad range of other multidimensional relaxation and diffusion experiments.