New structures in the bi­pyridine–copper(II) nitrate–methanol system: [(bpy)2Cu(NO3)]NO3·CH3OH and [(bpy)2Cu(NO3)]NO3

Reaction of 2,2′‐bi­pyridine (bpy) and copper(II) nitrate in methanol results in two complexes, namely light‐blue bis(2,2′‐bi­pyridine)­nitrato­copper(II) nitrate methanol solvate, [Cu(NO₃)(C₁₀H₈N₂)₂]NO₃·CH₃OH, (I), which is unstable in air, and the product of its decomposition, catena‐poly­[[[bis(2,2′‐bi­pyridine)copper(II)]‐μ‐nitrato‐O:O′] nitrate], {[Cu(NO₃)(C₁₀H₈N₂)₂]NO₃}_n, (II). The crystal structures of both compounds were determined from one crystal at room temperature. Later, the structure of (I) was redetermined at low temperature. In (I) and (II), the Cu atom is coordinated by two bpy and one or two nitrate ions, respectively. The second nitrate ion in (I), along with the methanol solvent mol­ecule, is found in the outer coordination sphere, not bonded to Cu. The nitrate in (I) is chelating, while in (II), it bridges (bpy)₂Cu complexes, forming a one‐dimensional chain structure. The Cu cation in (II) lies on a twofold axis and the uncoordinated NO₃^? ion is located close to a twofold axis and is therefore disordered. Compound (I) converts into (II) upon loss of solvent.     

Elucidating the initial dynamics of electron photodetachment from atoms in liquids using variably-time-delayed resonant multiphoton ionization

We study the photodetachment of electrons from sodium anions in room temperature liquid tetrahydrofuran (THF) using a new type of three-pulse pump-probe spectroscopy. Our experiments use two variably-time-delayed pulses for excitation in what is essentially a resonant 1+1 two-photon ionization: By varying the arrival time of the second excitation pulse, we can directly observe how solvent motions stabilize and trap the excited electron prior to electron detachment. Moreover, by varying the arrival times of the ionization (excitation) and probe pulses, we also can determine the fate of the photoionized electrons and the distance they are ejected from their parent Na atoms. We find that as solvent reorganization proceeds, the second excitation pulse becomes less effective at achieving photoionization, and that the solvent motions that stabilize the excited electron following the first excitation pulse occur over a time of approximately 450 fs. We also find that there is no spectroscopic evidence for significant solvent relaxation after detachment of the electron is complete. In combination with the results of previous experiments and molecular dynamics simulations, the data provide new insight into the role of the solvent in solution-phase electron detachment and charge-transfer-to-solvent reactions.     

Temperature effects for isothermal polymer crystallization kinetics

We adopt the cluster size distribution model to investigate the effect of temperature on homogeneous nucleation and crystal growth for isothermal polymer crystallization. The model includes the temperature effects of interfacial energy, nucleation rate, growth and dissociation rate coefficients, and equilibrium solubility. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different temperatures. The denucleation (Ostwald ripening effect) is also investigated by comparing moment and numerical solutions of the population balance equations. Agreement between the model results and temperature-sensitive experimental measurements for different polymer systems required strong temperature dependence for the crystal-melt interfacial energy.     

Application of relaxation periods during electrodialysis of a casein solution: Impact on anion-exchange membrane fouling

Electrodialysis (ED) is a membrane process used on a large scale. However, one of the common problems is fouling of ion-exchange membranes stacked in the cell. The use of pulsed power, consisting in applying a constant current density during a fixed time of application (T_on) followed by a pause duration (T_off), was demonstrated recently as an effective fouling mitigation method for electrodialysis. Up until now, no work has investigated the potential of electrodialysis using pulsed electric field on protein fouling. The aim of the present work was to study the influence of pulsed electric field (PEF) with a low frequency square shaped periodic signal (T_on = 10 s–T_off = 10 s, T_on = 10 s–T_off = 40 s) in comparison with dc current during electrodialysis of a casein solution at different current densities (10, 20 and 30 mA/cm²) on membrane fouling. It appeared from these results that PEF, under certain conditions of pulse, would avoid fouling on anion-exchange membranes. For 10 s–40 s pulsed electric field conditions, no fouling was observed with any density, while for 10 s–10 s PEF conditions, fouling appeared only at current density over 10 mA/cm². dc current, whatever the current density conditions, led to a fouling on the diluate side of the AEM. Furthermore, when fouling occurred, magnitude layer thickness and dry weight increased with the applied current density. The nature of the fouling was identified as 97% protein. The protein fouling would be due to the dissociation of water molecules and/or heat increase at the anion-exchange membrane interface. The relaxation time of the pulse would limit both phenomena on the membrane.     

Splitting‐characterizations of the Papangelou process

For point processes we establish a link between integration‐by‐parts‐ and splitting‐formulas which can also be considered as integration‐by‐parts‐formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Pólya and Gibbs processes.     

A topological characterization of the Sierpiński triangle

We present a topological characterization of the Sierpiński triangle. This answers question 58 from the Problem book of the Open Problem Seminar held at Charles University. In fact we give a characterization of the Apollonian gasket first. Consequently we show that any subcontinuum of the Apollonian gasket, whose boundary consists of three points, is homeomorphic to the Sierpiński triangle.