Influence of connectivity and porosity on ligand-based luminescence in zinc metal-organic frameworks

Applications of metal-organic frameworks (MOFs) require close correlation between their structure and function. We describe the preparation and characterization of two zinc MOFs based on a flexible and emissive linker molecule, stilbene, which retains its luminescence within these solid materials. Reaction of trans-4,4'-stilbene dicarboxylic acid and zinc nitrate in N,N-dimethylformamide (DMF) yielded a dense 2-D network, 1, featuring zinc in both octahedral and tetrahedral coordination environments connected by trans-stilbene links. Similar reaction in N,N-diethylformamide (DEF) at higher temperatures resulted in a porous, 3-D framework structure, 2. This framework consists of two interpenetrating cubic lattices, each featuring basic zinc carboxylate vertices joined by trans-stilbene, analogous to the isoreticular MOF (IRMOF) series. We demonstrate that the optical properties of both 1 and 2 correlate with the local ligand environments observed in the crystal structures. Steady-state and time-resolved spectroscopic measurements reveal that the stilbene linkers in the dense structure 1 exhibit a small degree of interchromophore coupling. In contrast, the stilbenoid units in 2 display very little interaction in this low-density 3-D framework, with excitation and emission spectra characteristic of monomeric stilbenes, similar to the dicarboxylic acid in dilute solution. In both cases, the rigidity of the stilbene linker increases upon coordination to the inorganic units through inhibition of torsion about the central ethylene bond, resulting in luminescent crystals with increased emission lifetimes compared to solutions of trans-stilbene. The emission spectrum of 2 is found to depend on the nature of the incorporated solvent molecules, suggesting use of this or related materials in sensor applications.     

Rh(I)-catalyzed carbonylative ring opening of diazabicycles with acyl anion equivalents

A catalytic desymmetrization of strained alkenes by ring-opening of meso-diazabicycles with acyl anion nucleophiles is reported. Densely functionalized trans-1,2-hydrazinoacyl cyclopentene building blocks are obtained stereoselectively. The acyl anion equivalent is generated in situ under very mild conditions from readily available organoboron precursors.     

Theory of crystallizable block copolymers

We present an equilibrium theory of diblock copolymers in which one of the blocks is crystallizable and the other is amorphous. The material is assumed to order in a lamellar structure of alternating semi-crystalline and amorphous layers with the chemical bonds which connect the copolymer blocks lying in the interfacial regions between the layers. The amorphous blocks are modelled as flexible chains, each with one end (the joint) anchored in an interface. Their contribution to the free energy is calculated via the self-consistent solution of the modified diffusion equations. The crystalline regions are modelled as folded chains, also with one end in an interfacial region (bonded to the corresponding end of an amorphous block). We find that the calculated amorphous block-free energies can be expressed as a single universal function depending on the total degree of polymerization of the amorphous block, its stretching, and a parameter proportional to the thickness of the interface. We have fitted an analytical form to this function, which can be used for any amorphous block, and we have combined it with our model of the crystallizable block to obtain scaling laws describing the equilibrium morphology.     

Spontaneous macroscopic spin polarization in independent spinor Bose-Einstein condensates

We present experimental evidence for the spontaneous formation of a macroscopic spin polarization in overlapping regions of two independent Bose-Einstein condensates produced in different hyperfine states of 87Rb. The condensates are independent in the sense that we do not explicitly introduce a relative phase between them. A single "spin-tip" pulse maps the transverse spin polarization into longitudinal spin polarization, and the atomic density distributions are measured with a Stern-Gerlach imaging method. The resulting matter-wave interference patterns are anticorrelated.     

A high-throughput search for direct methanol fuel cell anode electrocatalysts of type PtxBiyPbz

We used a high-throughput method to screen for direct methanol fuel cell anode electrocatalysts in the Pt-Bi-Pb system. Previous studies showed that PtBi and PtPb (both NiAs structure type) were active electrocatalysts for the oxidation of formic acid, but only PtPb was active in oxidizing methanol. We synthesized thin films with continuous composition spreads of the three elements by magnetron sputtering at deposition temperatures from ambient to 510 °C. A fluorescence method was then used to identify compositions that were active toward methanol oxidation. Only films deposited between temperatures of 160 and 400 °C showed electrocatalytic activity. The areas that were active for methanol oxidation showed predominantly the NiAs structure type according to XRD, with optimal activity for compositions near PtBi_0.01Pb_0.53.     

Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.     

Simultaneous detection of resolved glutamate, glutamine, and gamma-aminobutyric acid at 4 T

A new approach is introduced to simultaneously detect resolved glutamate (Glu), glutamine (Gln), and gamma-aminobutyric acid (GABA) using a standard STEAM localization pulse sequence with the optimized sequence timing parameters. This approach exploits the dependence of the STEAM spectra of the strongly coupled spin systems of Glu, Gln, and GABA on the echo time TE and the mixing time TM at 4 T to find an optimized sequence parameter set, i.e., {TE, TM}, where the outer-wings of the Glu C4 multiplet resonances around 2.35 ppm, the Gln C4 multiplet resonances around 2.45 ppm, and the GABA C2 multiplet resonance around 2.28 ppm are significantly suppressed and the three resonances become virtual singlets simultaneously and thus resolved. Spectral simulation and optimization were conducted to find the optimized sequence parameters, and phantom and in vivo experiments (on normal human brains, one patient with traumatic brain injury, and one patient with brain tumor) were carried out for verification. The results have demonstrated that the Gln, Glu, and GABA signals at 2.2-2.5 ppm can be well resolved using a standard STEAM sequence with the optimized sequence timing parameters around {82 ms,48 ms} at 4 T, while the other main metabolites, such as N-acetyl aspartate (NAA), choline (tCho), and creatine (tCr), are still preserved in the same spectrum. The technique can be easily implemented and should prove to be a useful tool for the basic and clinical studies associated with metabolism of Glu, Gln, and/or GABA.     

Some calculable contributions to entanglement entropy

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry: its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.     

Addison-type series representation for the Stieltjes constants

The Stieltjes constants γk(a) appear in the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(s,a) about its only pole at s=1. We generalize a technique of Addison for the Euler constant γ=γ₀(1) to show its application to finding series representations for these constants. Other generalizations of representations of γ are given.     

The algebraic structure of cohomological field theory

The algebraic foundation of cohomological field theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occuring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.