Parabolic conjugacy in general linear groups

Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL _n (q). We show that the number of P(q)-conjugacy classes in GL _n (q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006)     

Studies on the preparation and characterization of monodisperse polystyrene latices. VI. Preparation of zwitterionic latices

The preparation of zwitterionic latex particles is reported by using a mixed anionic and cationic initiator system without requiring surface-active agents. Isoelectric points were found from microelectrophoresis experiments and were in the pH range of 3.5-5. Close to the isoelectric point, the latices coagulated as expected, and good stability was achieved outside this narrow range. This range of stability was in good agreement with predictions from current theory. Redispersion after coagulation was found to be difficult as was expected for a hydrophobic colloid. The electrokinetic behavior did not result in the maximum in zeta potential at an electrolyte concentration of 1 mM unlike the situation for other hydrophobic polystyrene latex particles, and hence these systems may be even better models for other colloidal studies.     

Metal-metal charge transfer and solvatochromism in cyanomanganese carbonyl complexes of ruthenium and osmium

The complexes [(H3N)5Ru(II)(mu-NC)Mn(I)Lx]2+, prepared from [Ru(OH2)(NH3)5]2+ and [Mn(CN)L(x)] {L(x) = trans-(CO)2{P(OPh)3}(dppm); cis-(CO)2(PR3)(dppm), R = OEt or OPh; (PR3)(NO)(eta-C5H4Me), R = Ph or OPh}, undergo two sequential one-electron oxidations, the first at the ruthenium centre to give [(H3N)5Ru(III)(mu-NC)Mn(I)Lx]3+; the osmium(III) analogues [(H3N)5Os(III)(mu-NC)Mn(I)Lx]3+ were prepared directly from [Os(NH3)5(O3SCF3)]2+ and [Mn(CN)Lx]. Cyclic voltammetry and electronic spectroscopy show that the strong solvatochromism of the trications depends on the hydrogen-bond accepting properties of the solvent. Extensive hydrogen bonding is also observed in the crystal structures of [(H3N)5Ru(III)(mu-NC)Mn(I)(PPh3)(NO)(eta-C5H4Me)][PF6]3.2Me2CO.1.5Et2O, [(H3N)5Ru(III)(mu-NC)Mn(I)(CO)(dppm)2-trans][PF6]3.5Me2CO and [(H3N)5Ru(III)(mu-NC)Mn(I)(CO)2{P(OEt)3}(dppm)-trans][PF6]3.4Me2CO, between the amine groups (the H-bond donors) at the Ru(III) site and the oxygen atoms of solvent molecules or the fluorine atoms of the [PF6]- counterions (the H-bond acceptors).     

Magnetic structure of MnO at 10 K from total neutron scattering data

Total neutron scattering data from a powdered sample of MnO collected at 10 K have been analyzed using the reverse Monte Carlo method to refine the nuclear and magnetic structure. The results give the first unambiguous assignment of the average magnetic structure. The magnetic moments are aligned ferromagnetically within (111) sheets with the magnetization vectors of alternate sheets along axes parallel and antiparallel to the <112> directions, albeit with a small modulated out-of-plane component. Small displacements of Mn and O (modulated with the same periodicity) accompany the magnetic ordering and both atomic and magnetic structures may be described in the monoclinic space group C2.     

Control of Metal–Organic Framework Crystallization by Metastable Intermediate Pre‐equilibrium Species

There is an increasing amount of interest in metal–organic frameworks (MOFs) for a variety of applications, from gas sensing and separations to electronics and catalysis. However, the mechanisms by which they crystallize remain poorly understood. Herein, an important new insight into MOF formation is reported. It is shown that, prior to network assembly, crystallization intermediates in the canonical ZIF‐8 system exist in a dynamic pre‐equilibrium, which depends on the reactant concentrations and the progress of reaction. Concentration can, therefore, be used as a synthetic handle to directly control particle size, with potential implications for industrial scale‐up and gas sorption applications. These findings enable the rationalization of apparent contradictions between previous studies of ZIF‐8 and opens up new opportunities for the control of crystallization in network solids more generally.     

Light Lanthanide Metallocenium Cations Exhibiting Weak Equatorial Anion Interactions

As the dysprosocenium complex [Dy(Cp^ttt)₂][B(C₆F₅)₄] (Cp^ttt=C₅H₂tBu₃-1,2,4, 1-Dy ) exhibits magnetic hysteresis at 60 K, similar lanthanide (Ln) complexes have been targeted to provide insights into this remarkable property. We recently reported homologous [Ln(Cp^ttt)₂][B(C₆F₅)₄] ( 1-Ln ) for all the heavier Ln from Gd–Lu; herein, we extend this motif to the early Ln. We find, for the largest Ln^III cations, that contact ion pairs [Ln(Cp^ttt)₂{(C₆F₅-κ¹-F)B(C₆F₅)₃}] ( 1-Ln ; La–Nd) are isolated from reactions of parent [Ln(Cp^ttt)₂(Cl)] ( 2-Ln ) with [H(SiEt₃)₂][B(C₆F₅)₄], where the anion binds weakly to the equatorial sites of [Ln(Cp^ttt)₂]⁺ through a single fluorine atom in the solid state. For smaller Sm^III, [Sm(Cp^ttt)₂][B(C₆F₅)₄] ( 1-Sm ) is isolated, which like heavier 1-Ln does not exhibit equatorial anion interactions, but the Eu^III analogue 1-Eu could not be synthesised due to the facile reduction of Eu^III precursors to Eu^II products. Thus with the exception of Eu and radioactive Pm this work constitutes a structurally similar family of Ln metallocenium complexes, over 50 years after the [M(Cp)₂]⁺ series was isolated for the 3d metals.     

Crystal structure of (4α,4aα,8aα)-(±)-octahydro-2-(phenylmethyl)-2H-1,2-benzoxazin-4-ol, 4-methylbenzenesulfonate(ester)

The title compound, a bicyclic tetrahydro-1,2-oxazine, crystallizes in a monoclinic lattice, space group P2₁/c, with a = 12.9809(18)Å, b = 12.920(2)Å, c = 13.631(2)Å, = 110.713(12)°, and Z = 4. The structure found in the solid state for this conformationally mobile molecule shows the tosyl group in an axial position and a benzyl group in an equatorial position of the bicyclic system.