Influence of pH and counteranion on the structure of tropolonato-lead(II) complexes: structural and infrared characterization of formed lead compounds

Reactions of tropolone with lead(II) trifluoromethanesulfonate, perchlorate, and nitrate in water/methanol mixtures at pH below 1.0 lead to the formation of three different polymeric lead(II) complexes, [Pb(trop)(CF3SO3)(H2O)]n (1), [Pb3(trop)4(ClO4)2]n (2), and [Pb2(trop)2(NO3)2(CH3OH)]n (3), respectively. On the other hand, if the reactions are performed at pH above 2.0, the dimeric compound [Pb(trop)2]2 (4) is obtained independently of the lead(II) salt used, as long as lead(II) does not form any strong complexes with the counterion. The crystal structures of these compounds have been determined by single-crystal X-ray diffraction. The structure of solid tetrakis(tropolonato)lead(IV), Pb(trop)4 (5), has been studied by means of the EXAFS technique because it was not possible to obtain sufficiently large single crystals. In the polymeric structures, the counterions are coordinated to the lead(II) ions and act as bridges. The tropolonato ligand behaves as a chelating agent and a tri- or tetraconnective bridge. The total coordination number of the lead(II) ion is five in compound 4, seven in 1 and 3, and eight in 2, and the lead(IV) ion in 5 is eight-coordinated. The 6s2 lone electron pair on the lead(II) ion seems to be stereochemically active in all lead(II) complexes studied. All compounds have been characterized by IR spectroscopy as well.     

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.     

Self‐Directed Teacher Learning in Collaborative Contexts

Two related case studies of secondary mathematics teachers examine the roles and conditions helpful in initiating, directing, and/or supporting teachers' own professional development. Using multiple data sources from school‐based and professional settings, we applied analytic induction to identify patterns of similarities and differences in teachers' experiences and developmental trajectories. Findings revealed how the teachers served as brokers in their own development process and how attitude, attention, and awareness played important roles in teacher learning. As the teachers initiated learning processes, they demonstrated awareness of broader educational contexts that support learning by identifying external policies and priorities that aligned with teachers' attitudes. They then used these external priorities as boundary objects to broker for teachers' learning, including other teachers' learning. They attended to learning needs in directing a plan for learning activities, rather than using externally mandated goals for changing practice (e.g., an external focus on improving students' tests scores). These cases suggest that in structuring professional learning, opportunities to self‐identify learning needs should be part of the process, and external supports can become more powerful when teachers play a brokering role in relating these supports to their immediate contexts. Further implications for professional development processes are explored.     

An inverse problem for infinitely divisible moving average random fields

Statistical Inference for Stochastic Processes - Given a low frequency sample of an infinitely divisible moving average random field $${int _{mathbb {R}^d} f(x-t)varLambda (dx); t in mathbb...     

Shaping of intense ion beams into hollow cylindrical form

A specifically tailored plasma lens could shape a high-energy, heavy-ion beam into the form of a hollow cylinder without loss of beam intensity. It has been experimentally confirmed that both a positive as well as a negative radial gradient of the current density in the active plasma lens can be the underlying principle. Calculations were performed that yield the ideal current density distribution for both cases. A numerical simulation of an experiment with an intense ion beam highlights that the shaping of the beam increases the achievable compression in a lead sample.     

Chromatographic size separation of single-wall carbon nanotubes

Received: 18 May 1998/Accepted: 22 May 1998