Disappearing Polymorphs in Metal–Organic Framework Chemistry: Unexpected Stabilization of a Layered Polymorph over an Interpenetrated Three-Dimensional Structure in Mercury Imidazolate

The “disappearing polymorph” phenomenon is well established in organic solids, and has had a profound effect in pharmaceutical materials science. The first example of this effect in metal-containing systems in general, and in coordination-network solids in particular, is here reported. Specifically, attempts to mechanochemically synthesize a known interpenetrated diamondoid (dia) mercury(II) imidazolate metal–organic framework (MOF) yielded a novel, more stable polymorph based on square-grid (sql) layers. Simultaneously, the dia-form was found to be highly elusive, observed only as a short-lived intermediate in monitoring solvent-free synthesis and not at all from solution. The destabilization of a dense dia-framework relative to a lower dimensionality one is in contrast to the behavior of other imidazolate MOFs, with periodic density functional theory (DFT) calculations showing that it arises from weak interactions, including structure-stabilizing agostic C−H⋅⋅⋅Hg contacts. While providing a new link between MOFs and crystal engineering of organic solids, these findings highlight a possible role for agostic interactions in directing topology and stability of MOF polymorphs.     

A generalization of Serre’s condition $$\mathrm {(F)}$$ ( F ) with applications to the finiteness of unramified cohomology

Mathematische Zeitschrift - In this paper, we introduce a condition ( $$\mathrm {F}_m'$$ ) on a field K, for a positive integer m, that generalizes Serre’s condition (F) and which still...     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.     

Intra‐ and inter‐supramolecular complexation of poly(butyl methacrylate)‐co‐2‐(1,2,3‐triazol‐4‐yl)pyridine copolymers induced by CoII,FeII, and EuIII ions monitored by molecular hydrodynamics methods

Poly(butyl methacrylate) copolymers embedding bidentate 2‐(1,2,3‐triazol‐4‐yl)pyridine (trzpy) chelating units as comonomer in the side chains were synthesized by controlled radical addition‐fragmentation transfer (RAFT) polymerization. Intracomplexation and intercomplexation of the macromolecules of the poly(butyl methacrylate) copolymers containing 20 % mol of trzpy units induced by Co^II, Fe^II, and Eu^III ions were studied in the solutions by macromolecular hydrodynamics methods. The sedimentation velocity of extremely diluted copolymer solutions and the dynamic viscosity of moderately diluted solutions were studied in a wide range of the salts concentrations. Differences were observed with respect to the copolymer behavior in the presence of the Co²⁺, Fe²⁺, Eu³⁺ ions. These differences are namely due to the differences in the number of coordination bonds required for complex formation and not explicitly to the nature of the corresponding anions. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2632–2639     

Aerosol retrievals from channel-1 and -2 AVHRR radiances: Long-term trends updated and revisited

The nominal Global Aerosol Climatology Project (GACP) record of aerosol optical thickness (AOT) and Ångström exponent (AE) over the oceans is extended by 6 months to cover the period from August 1981 through December 2005. The most recent 4-year segment reveals no significant short-term tendencies in globally and hemispherically averaged AOTs and AEs. This finding is consistent with contemporaneous MODIS and MISR results and the accumulating evidence of a gradual transition from global brightening to global dimming. We also analyze the retrieval implications of allowing the imaginary part of the aerosols refractive index Im(m) to change over the duration of the GACP record. Our sensitivity study shows that increasing Im(m) from 0.003 during the 4-year pre-Pinatubo period up to 0.007 during the most recent 4-year segment of GACP data eliminates the previously identified long-term decreasing AOT trend. Should this long-term trend in Im(m) be real then it would cause the global absorption AOT over the oceans to more than double and the global single-scattering albedo to decrease from ～0.95 to ～0.88. Such changes could make tropospheric aerosols significant contributors to the recent surface temperature increase.     

Bound entangled states of four qubits in the tomographic-probability representation

We discuss the entanglement phenomenon on the example of the Smolin state of four qubits. This state is known as the bound entangled state and its spin tomogram is found in an explicit form. We apply the qubit-portrait method for investigating the violation of the Bell inequalities, since this approach provides another tool to prove the entanglement properties of the four-qubit state under consideration.