Crystal structures of two isostructural compounds: a second polymorph of dipotassium hydrogen citrate,K2HC6H5O7, and potassium rubidium hydrogen citrate,KRbHC6H5O7

The crystal structures of a new polymorph of dipotassium hydrogen citrate, 2K⁺·HC₆H₅O₇^2?, and potassium rubidium hydrogen citrate, K⁺·Rb⁺·HC₆H₅O₇^2?, have been solved and refined using laboratory powder X‐ray diffraction and optimized using density functional techniques. In the new polymorph of the dipotassium salt, KO₇ and KO₈ coordination polyhedra share corners and edges to form a three‐dimensional framework with channels parallel to the a axis and [111]. The hydrophobic methylene groups face each other in the channels. The un‐ionized carboxylic acid group forms a strong charge‐assisted hydrogen bond to the central ionized carboxylate group. The hydroxy group forms an intermolecular hydrogen bond to a different central carboxylate group. In the potassium rubidium salt, the K⁺ and Rb⁺ cations are disordered over two sites, in approximately 0.72:0.28 and 0.28:0.72 ratios. KO₈ and RbO₉ coordination polyhedra share corners and edges to form a three‐dimensional framework with channels parallel to the a axis. The un‐ionized carboxylic acid group forms a strong charge‐assisted hydrogen bond to an ionized carboxylate group. The hydroxy group forms an intermolecular hydrogen bond to the central carboxylate group. Density functional theory (DFT) calculations on the ordered cation structures suggest that interchange of K⁺ and Rb⁺ at the two cation sites changes the energy insignificantly.     

A generalization of regular convolutions and Ramanujan sums

The Ramanujan Journal - Regular convolutions of arithmetical functions were first defined by Narkiewicz (Colloq Math 10:81–94, 1963). Useful identities regarding generalizations of the...     

Spectroscopic and Crystallographic Characterization of the R3N+−C−H⋅⋅⋅X Interaction

As appreciation for nonclassical hydrogen bonds has progressively increased, so have efforts to characterize these interesting interactions. Whereas several kinds of C−H hydrogen bonds have been well-studied, much less is known about the R₃N⁺−C−H⋅⋅⋅X variety. Herein, we present crystallographic and spectroscopic evidence for the existence of these interactions, with special relevance to Selectfluor chemistry. Of particular note is the propensity for Lewis bases to engage in nonclassical hydrogen bonding over halogen bonding with the electrophilic F atom of Selectfluor. Further, the first examples of ¹H NMR experiments detailing R₃N⁺−C−H⋅⋅⋅X (X=O, N) hydrogen bonds are described.     

One‐Step Pyro‐Synthesis of a Nanostructured Mn3O4/C Electrode with Long Cycle Stability for Rechargeable Lithium‐Ion Batteries

A nanostructured Mn₃O₄/C electrode was prepared by a one‐step polyol‐assisted pyro‐synthesis without any post‐heat treatments. The as‐prepared Mn₃O₄/C revealed nanostructured morphology comprised of secondary aggregates formed from carbon‐coated primary particles of average diameters ranging between 20 and 40 nm, as evidenced from the electron microscopy studies. The N₂ adsorption studies reveal a hierarchical porous feature in the nanostructured electrode. The nanostructured morphology appears to be related to the present rapid combustion strategy. The nanostructured porous Mn₃O₄/C electrode demonstrated impressive electrode properties with reversible capacities of 666 mAh g^?1 at a current density of 33 mA g^?1, good capacity retentions (1141 mAh g^?1 with 100 % Coulombic efficiencies at the 100^th cycle), and rate capabilities (307 and 202 mAh g^?1 at 528 and 1056 mA g^?1, respectively) when tested as an anode for lithium‐ion battery applications.     

Ferroelectric Coordination Polymers Self‐Assembled from Mesogenic Zinc(II) Porphyrin and Dipolar Bridging Ligands

A new class of ferroelectric coordination‐based polymers has been developed by the self‐assembly of lipophilic zinc porphyrin ( ZnP ) and ditopic bridging ligands. The ligands contain dipolar benzothiadiazole or fluorobenzene units, which are axially coordinated to ZnP with the dipole moments oriented perpendicular to the coordination axes. The coordination‐based polymers show ferroelectric characteristics in the liquid crystalline state, as revealed by distinctive hysteresis in the polarization–electric field (P–E) loops and inversion current peaks in current–voltage (I–V) loops. The observed ferroelectric properties are explainable by flip–flop rotation of the dipolar axle ligands induced by the applied electric field, as demonstrated by the positive‐up–negative‐down (PUND) measurements. The present system provides a new operating principle in supramolecular ferroelectrics.     

On the non-emptiness of the one-core and the bargaining set of committee games

We study the committee decision making process using game theory. Shenoy  [15] introduced two solution concepts: the one-core and the bargaining set, and showed that the one-core of a simple committee game is nonempty if there are at most four players. We extend this result by proving that whether the committee is simple or not, as far as there are less than five players, the one-core is nonempty. This result also holds for the bargaining set.     

Monomer relative affinity in a copolymer

This paper analyzes data from experiments on simple polymer chains. It measures the extent to which a particular monomer prefers to link with another of the same type. To analyze the data, it derives the likelihood function for a two‐state Markov model in which only the number in each state, but not the order, is observed. This technology is applied to a data set on which experimenters mixed lactic‐glycolic monomers with a known proportion of a contaminant consisting of an extra lactic acid. The resulting copolymers were subjected to matrix‐assisted laser desorption ionization mass spectrometry. This records the number of copolymers at each atomic weight, which can be associated with a given length of copolymer and number of contaminant monomers. Analysis of the data shows that the proportion of contaminant monomers exceeded the proportion of experimentally induced contaminant. Maximum likelihood estimates using the data show that lactic‐glycolic monomers show a positive affinity for the contaminant. Copyright © 2015 John Wiley & Sons, Ltd.     

Nanoporous Materials Can Tune the Critical Point of a Pure Substance

Molecular simulations and NMR relaxometry experiments demonstrate that pure benzene or xylene confined in isoreticular metal–organic frameworks (IRMOFs) exhibit true vapor–liquid phase equilibria where the effective critical point may be reduced by tuning the structure of the MOF. Our results are consistent with vapor and liquid phases extending over many MOF unit cells. These results are counterintuitive since the MOF pore diameters are approximately the same length scale as the adsorbate molecules. As applications of these materials in catalysis, separations, and gas storage rely on the ability to tune the properties of adsorbed molecules, we anticipate that the ability to systematically control the critical point, thereby preparing spatially inhomogeneous local adsorbate densities, could add a new design tool for MOF applications.     

Analysis of ethyl glucuronide and ethyl sulfate using aqueous normal‐phase chromatography with mass spectrometry

The use of aqueous normal‐phase chromatography is explored as a possible format for the analysis of the forensically significant compounds ethyl glucuronide and ethyl sulfate. Standard solutions of the two compounds are used to verify the retention capabilities of two stationary phases (diamond hydride and undecanoic acid). These results are then compared to data obtained on hair extracts to determine if any matrix effects exist with respect to both retention and peak shape. The undecanoic stationary phase is used for the establishment of calibration curves for quantitative analysis. These curves are utilized to determine the concentration of ethyl glucuronide in several hair samples tested.