Multiple conformations of benzil in resorcinarene-based supramolecular host matrixes

Six supramolecular complexes incorporating benzil as a guest, CMCR*bipy*benzil (alpha) 1 (CMCR = C-methylcalix[4]resorcinarene), CMCR*bipy*benzil (beta) 2, CMCR*2bpe*benzil*ethanol 3 (bpe = trans-1,4-bis(pyridyl)ethylene), CMCR*2bpe*benzil*2H2O 4, CMCR.2bpeh*benzil*ethanol 5 (bpeh = bis-(1-pyridin-4-yl-ethylidene)-hydrazine), and CECR*2bpe.benzil 6 (CECR = C-ethylcalix[4]resorcinarene), have been synthesized by hydrothermal and conventional methods and characterized by X-ray diffraction. Resorcinarene adopts a boat conformation in 1-4 and a bowl conformation in 5 and 6. Compounds 1-4 show a brick-wall-like framework, in which two benzil molecules are incorporated. For 5, bpeh spacers link CMCR molecules to give a one-dimensional wavelike polymer in which one benzil guest is embedded within the polymer cavity. Complex 6 forms a carcerand-like capsule in which two benzil guests are encapsulated. The O=C-C=O torsion angles vary from 91.8 to 139.3 degrees and correlate with the length of the central C-C bond. The benzil concentration, which is approximately 6.2 mol/L in the neat crystals, varies between 1.01 and 1.51 mol/L in the structures studied, corresponding to a 6-fold dilution. The benzil molecules are disordered in the larger cavities of 4 and 5. The two benzoyl fragments are almost perpendicular in 3, which has the next largest cavity size when solvent volume is excluded, whereas a nearly trans-coplanar conformation occurs for the cavity with the smallest volume in 6.     

Effects of surface roughness on self- and transport diffusion in porous media in the Knudsen regime

The effect of surface roughness on Knudsen diffusion in nanoporous media is investigated by means of dynamic Monte Carlo simulations in three-dimensional rough fractal pores. These simulations yield new insight and explain a number of apparent inconsistencies by revealing a striking difference between the roughness dependence of transport diffusion and gradientless (self- or tracer) diffusion. Both analytical and simulation results show a significant roughness dependence of self-diffusion in the Knudsen regime. Transport diffusion, on the other hand, is roughness independent, as the fluxes do not depend on the detailed residence time and molecular trajectories.     

Space models of degree g+1 of curves of genus g

It is the aim of this note to determine all smooth curves of genus g admitting a birational space model of degree g + 1 whose plane sections define a complete linear series. And we add criteria when there is a smooth such model.     

Pencils on separating (M-2)-curves

A separating ( \(M-2\) )-curve is a smooth geometrically irreducible real projective curve \(X\) such that \(X(\mathbb{R })\) has \(g-1\) connected components and \(X(\mathbb{C })\setminus X(\mathbb{R })\) is disconnected. Let \(T_g\) be a Teichmüller space of separating ( \(M-2\) )-curves of genus g. We consider two partitions of \(T_g\) , one by means of a concept of special type, the other one by means of the separating gonality. We show that those two partitions are very closely related to each other. As an application, we obtain the existence of real curves having isolated real linear systems \(g^1_{g-1}\) for all \(g\ge 4\) .     

Multiperiodic multifractal martingale measures

A nonnegative 1-periodic multifractal measure on is obtained as infinite random product of harmonics of a 1-periodic function W(t). Such infinite products are statistically self-affine and generalize certain Riesz products with random phases. They are martingale structures, therefore converge. The criterion on W for nondegeneracy is provided. It differs completely from those for other known random measures constructed as martingale limits of multiplicative processes. In particular, it is very sensitive to small changes in W(t). When these infinite products are interpreted in the framework of thermodynamic formalism for random transformations, logW is a potential function when W>0. For regular enough potentials, in case of degeneracy, the natural normalization makes the sequence of measures converge. Moreover, this normalization is neutral for nondegenerate martingales. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points.     

How Does Substitutional Doping Affect Visible Light Absorption in a Series of Homodisperse Ti11 Polyoxotitanate Nanoparticles?

Homodisperse doped polyoxotitanate nanoclusters with formulae Ti₁₁(MX)O₁₄(OiPr)₁₇ (M=Mn, Fe or Co; X=Cl, Br or I, OiPr=isopropoxide) display strongly dopant‐dependent properties. Spectroscopic solution and reflectance measurements backed up by density of states and time‐dependent DFT calculations based on the determined structures, show the prominent effect of FeX substitution by decreasing the HOMO–LUMO gap of the particles. The effect is attributed to the presence of an occupied Fe β orbital halfway up the bandgap, leading to long‐wavelength absorption with electron transfer to the titanium atoms of the cluster. Whereas the light absorption varies significantly with variation of the transition metal dopant, its dependency on the nature of the halogen atom or the change in dipole moment across the series is minor.