Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Host–Guest Chemistry of a Bis‐Calix[4]pyrrole Derivative Containing a trans/cis‐Switchable Azobenzene Unit with Several Aliphatic Bis‐Carboxylates

The azobenzene unit used as a photochemically and thermally switchable linker in the assembly of a bis‐calix[4]pyrrole receptor provides a means to modulate the binding of bis‐carboxylates of significant biological importance in cancer research. Conversely, the complexation of different bis‐anionic guests has significant kinetic effects on both the photochemical and thermal trans/cis isomerization of the azobenzene unit.     

Highly fluorescent polycaprolactones decorated with di(thiophene‐2‐yl)‐diketopyrrolopyrrole: A covalent strategy of tuning fluorescence properties in solid states

Well‐defined 1,4‐diketo‐3,6‐di(thiophen‐2‐yl)pyrrolo[3,4‐c]pyrrole (DTDPP) labeled polycaprolactones (PCL) with different chain lengths were synthesized and characterized. The effect of polymer chain lengths on the optical properties of DTDPP in solid states was studied by UV‐Vis absorption spectroscopy as well as steady‐state and dynamic fluorescence spectroscopies. Our results indicate that when the PCL side chain is extended to a certain length, the intermolecular aggregation of DTDPP units can be reduced significantly due to segregation effect of PCL. This approach offers a new facile strategy to address the common problem of aggregation‐caused quenching existing in organic fluorophores. These highly fluorescent biodegradable PCL polymers may find broad biomedical applications such as fluorescence‐based bioimaging and tissue engineering. © 2015 Wiley Periodicals, Inc. J. Polym. Sci. Part A: Polym. Chem. 2015 , 53, 1032–1042     

Supramolecular Recognition Influences Magnetism in [X@HVIV8VV14O54]6− Self‐Assemblies with Symmetry‐Breaking Guest Anions

Mixed‐valence polyoxovanadates(IV/V) have emerged as one of the most intricate class of supramolecular all‐inorganic host species, able to encapsulate a wide variety of smaller guest templates during their self‐assembly formation process. As showcased herein, the incorporation of guests, though governed solely by ultra‐weak electrostatic and van der Waals interactions, can cause drastic effects on the electronic and magnetic characteristics of the shell complex of the polyoxovanadate. We address the question of methodology for the magnetochemical analysis of virtually isostructural {V^IV/V₂₂O₅₄}‐type polyoxoanions of D_2d symmetry enclosing diamagnetic VO₂F₂^? (C_2v), SCN^? (C_∞v), or ClO₄^? (T_d) template anions. These induce different polarization effects related to differences in their geometric structures, symmetry, ion radii, and valence shells, eventually resulting in a supramolecular modulation of magnetic exchange between the V(3d) electrons that are partly delocalized over the {V₂₂O₅₄} shells. We also include the synthesis and characterization of the novel [V^VO₂F₂@HV^IV₈V^V₁₄O₅₄]^6? system that comprises the rarely encountered discrete difluorovanadate anion as a quasi‐isolated guest species.     

Enhancing the Water Stability of Al‐MIL‐101‐NH2 via Postsynthetic Modification

The resistance of metal–organic frameworks towards water is a very critical issue concerning their practical use. Recently, it was shown for microporous MOFs that the water stability could be increased by introducing hydrophobic pendant groups. Here, we demonstrate a remarkable stabilisation of the mesoporous MOF Al‐MIL‐101‐NH₂ by postsynthetic modification with phenyl isocyanate. In this process 86 % of the amino groups were converted into phenylurea units. As a consequence, the long‐term stability of Al‐MIL‐101‐URPh in liquid water could be extended beyond a week. In water saturated atmospheres Al‐MIL‐101‐URPh decomposed at least 12‐times slower than the unfunctionalised analogue. To study the underlying processes both materials were characterised by Ar, N₂ and H₂O sorption measurements, powder X‐ray diffraction, thermogravimetric and chemical analysis as well as solid‐state NMR and IR spectroscopy. Postsynthetic modification decreased the BET equivalent surface area from 3363 to 1555 m² g^?1 for Al‐MIL‐101‐URPh and reduced the mean diameters of the mesopores by 0.6 nm without degrading the structure significantly and reducing thermal stability. In spite of similar water uptake capacities, the relative humidity‐dependent uptake of Al‐MIL‐101‐URPh is slowed and occurs at higher relative humidity values. In combination with ¹H‐²⁷Al D ‐HMQC NMR spectroscopy experiments this favours a shielding mechanism of the Al clusters by the pendant phenyl groups and rules out pore blocking.     

Development of Sulfonic-Acid-Functionalized Mesoporous Materials: Synthesis and Catalytic Applications

Sulfonic acid based mesostructures (SAMs) have been developed in recent years and have important catalytic applications. The primary applications of these materials are in various organic synthesis reactions, such as multicomponent reactions, carbon–carbon bond couplings, protection reactions, and Fries and Beckman rearrangements. This review aims to provide an overview of the recent developments in the field of SAMs with a particular emphasis on the reaction scope and advantages of heterogeneous solid acid catalysts.     

Fluorescence Properties and Exciplex Formation of Emissive Naphthyridine Derivatives: Application as Sensors for Amines

Water-soluble donor–acceptor-type fluorophore 15Nap-Cl having two trifluoromethyl groups and a Cl group on a 1,5-aminonaphthyridine framework was prepared. Fluorophore 15Nap-Cl showed strong solvatochromic fluorescence, and, as the solvent polarity increased, a bathochromic shift was observed accompanied by an increase in the fluorescence quantum yield. In addition, in the presence of amines such as ethylamine, diethylamine, and aniline, further considerable bathochromic shifts in the fluorescence were observed. Density functional calculations identified the source of the fluorescence behavior as exciplex formation between 15-Nap-Cl and the corresponding amine. The fluorescence behavior was exploited to fabricate a sensor that can identify various primary, secondary, and tertiary amines.     

Pentapnictogen heterocyclic monoanions: Structure,stability, and aromaticity

Inorganic planar ring-shape molecules with 4n + 2 π electrons are always the focus of experimental synthesis and theoretical research due to their potential aromaticity and stability. In this work, the whole series of five-membered heterocycle monoanions X _nY_5-n⁻ (X, Y = group 15 elements; n = 1-4) were thoroughly investigated by means of density functional theory calculations. They all have large formation energies and HOMO-LUMO gap energies, suggesting the potential thermodynamic and kinetic stability. Their aromaticities are comparable to that of typical aromatic hydrocarbons. Their thermal stabilities were firmly established by the ab initio molecular dynamics simulations. As most of them are predicted for the first time, their various spectra were simulated for experimental characterization. Furthermore, we demonstrate that these five-membered cyclic anions can be employed as η⁵-ligand to construct novel all-inorganic metallocenes, which may serve as the building blocks of low-dimensional nanomaterials.