Synthesis, structure, and dynamics of six-membered metallacoronands and metallodendrimers of iron and indium

In the reaction of the N-substituted diethanolamines (H(2)L(1-3)) (1-3) with calcium hydride followed by addition of iron(III) or indium(III) chloride, the iron wheels [Fe(6)Cl(6)(L(1))(6)] (4) and [Fe(6)Cl(6)(L(2))(6)] (6) or indium wheels [In(6)Cl(6)(L(1))(6)] (5), [In(6)Cl(6)(L(2))(6)] (8) and [In(6)Cl(6)(L(3))(6)] (9) were formed in excellent yields. Exchange of the chloride ions of 6 by thiocyanate ions afforded [Fe(6)(SCN)(6)(L(2))(6)] (7). Whereas the structures of 4, 5 and 7 were determined unequivocally by single-crystal X-ray analyses, complexes 8 and 9 were characterised by NMR spectroscopy. Contrary to what is normally presumed, the scaffolds of six-membered metallic wheels are not generally rigid, but rather undergo nondissociative topomerisation processes. This was shown by variable temperature (VT) (1)H NMR spectroscopy for the indium wheel [In(6)Cl(6)(L(1))(6)] (5) and is highlighted for the enantiotopomerisation of one indium centre [ 1/6[S(6)-5]<==>[1/6[S(6)-5']]. The self-assembly of metallic wheels, starting from diethanolamine dendrons, is an efficient strategy for the convergent synthesis of metallodendrimers.     

TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.     

Backstepping-based output regulation for systems with infinite-dimensional actuator and sensor dynamics

The output regulation problem is solved for an ODE plant driven by a parabolic actuator with spatially varying coefficients. Applying the backstepping transformation to the actuator allows the solution of the regulator equations in closed-form and thus the formulation of the solvability condition. An output feedback regulator is obtained by designing a disturbance observer using delayed measurement and a reference observer that both achieve finite-time convergence. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Field-induced texture conversions in smectic A,B and C phases

The field-induced texture conversions in smectic A, B and C phases were studied for 7 liquid crystalline compounds. The threshold voltage of the effect was measured in dependence on the temperature and the layer thickness. The results are discussed.