On Mixed Cages

Mixed graphs have both directed and undirected edges. A mixed cage is a regular mixed graph of given girth with minimum possible order. In this paper mixed cages are studied. Upper bounds are obtained by general construction methods and computer searches

On Mixed Cages of Girth 6

A [z,r;g]-mixed cage is a mixed graph of minimum order such that each vertex has z in-arcs, z out-arcs, r edges, and it has girth g. We present an infinite family of mixed graphs with girth 6. This construction also provides an upper bound on the minimum order of mixed cages of girth 6. Additionally,we introduce a lower bound on the minimum order for any mixed cage

Ultrafast IR spectroscopy of photo-induced electron transfer in self-assembled donor-acceptor coordination cages.

Photo-induced processes in self-assembled coordination cages were studied by femtosecond infrared pump-probe spectroscopy. Densely packed, interpenetrated double cages were constructed from eight bis-monodentate redoxactive ligands bound to four Pd(ii) nodes. Two types of ligands consisting of electron rich phenothiazine (PTZ) or electron deficient anthraquinone (ANQ) chromophores were used to assemble either homo-octameric or mixed-ligand cages. Upon photoexcitation the homo-octameric acceptor cage undergoes intersystem crossing to a long-lived triplet state, similar to the free acceptor ligand. Excitation of the free donor ligand leads to a fluorescent state with intramolecular charge transfer character. This fluorescence is completely quenched in the homo-octameric donor double cage due to a ligand-to-metal charge transfer followed by back electron transfer on a ps timescale. Only for the mixed-ligand cage irradiation produces a charge separated state with an oxidized PTZ radical cation and a reduced ANQ radical anion as proven by their vibrational fingerprints in the transient IR spectra. In dichloromethane the lifetime of this charge separated state extends from tens of ps to >1.5 ns which is attributed to the broad distribution of mixed-ligand cages with different stoichiometry and/or stereo configurations

Excitation Energy Delocalization and Transfer to Guests within M(II)4L6 Cage Frameworks

We have prepared a series of M(II)4L6 tetrahedral cages containing one or the other of two distinct BODIPY moieties, as well as mixed cages that contain both BODIPY chromophores. The photophysical properties of these cages and their fullerene-encapsulated adducts were studied in depth. Upon cage formation, the charge-transfer character exhibited by the bis(aminophenyl)-BODIPY subcomponents disappeared. Strong excitonic interactions were instead observed between at least two BODIPY chromophores along the edges of the cages, arising from the electronic delocalization through the metal centers. This excited-state delocalization contrasts with previously reported cages. All cages exhibited the same progression from an initial bright singlet state (species I) to a delocalized dark state (species II), driven by interactions between the transition dipoles of the ligands, and subsequently into geometrically relaxed species III. In the case of cages loaded with C60 or C70 fullerenes, ultrafast host-to-guest electron transfer was observed to compete with the excitonic interactions, short-circuiting the I → II → III sequence

Anisotropic polyoxometalate cages assembled via layers of heteroanion templates

The synthesis of anisotropic redox-active polyoxometalates (POMs) that can switch between multiple states is critical for understanding the mechanism of assembly of structures with a high aspect ratio, as well as for their application in electronic devices. However, a synthetic methodology for the controlled growth of such clusters is lacking. Here we describe a strategy, using the heteroanion-directed assembly, to produce a family of ten multi-layered anisotropic POM cages templated redox-active pyramidal heteroanions with the composition [W16Mo2O54(XO3)]n-,[W21Mo3O75(XO3)2]m-,[W26Mo4O93(XO3)3]o- for the single, double and triple layered clusters respectively. It was found that the introduction of reduced molybdate is essential for self-assembly of and results in mixed-metal (W/Mo) and mixed-valence (WVI/MoV) POM cages, as confirmed by an array of analytical techniques. To probe the archetype in detail, a tetrabutyl ammonium (TBA) salt derivative of a fully oxidized two-layered cage is produced as a model structure to confirm that all the cages are a statistical mixture of isostructures with variable ratios of W/Mo. Finally, it was found that multi-layered POM cages exhibit dipolar relaxations due to the presence of the mixed valence WVI/MoV metal centers, demonstrating their potential use for electronic materials

Jamming Percolation in Three Dimensions

We introduce a three-dimensional model for jamming and glasses, and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and glass-transitions, this is a mixed-order transition; the discontinuity is accompanied by diverging length- and time-scales. Because one-dimensional directed-percolation paths comprise the backbone of frozen particles, the unfrozen rattlers may use the third dimension to travel between their cages. Thus the dynamics are diffusive on long-times even above the critical density for jamming.Comment: 6 pages, 6 figure

The Surface Area to Volume Ratio Changes the Pharmacokinetic and Pharmacodynamic Parameters in the Subcutaneous Tissue Cage Model:As Illustrated by Carprofen in Sheep

Introduction: Pharmacokinetic and pharmacodynamic models can be powerful tools for predicting outcomes. Many models are based on repetitive sampling of the vascular space, due to the simplicity of obtaining samples. As many drugs do not exert their effect in the vasculature, models have been developed to sample tissues outside the bloodstream. Tissue cages are hollow devices implanted subcutaneously, or elsewhere, that are filled with fluid allowing repetitive sampling to occur. The physical dimensions of the cage, namely, the diffusible surface area to volume ratio, would be expected to change the rate of drug movement into and out of tissue cages. Methods: Seven sheep were implanted with five pairs of tissue cages, subcutaneously. Each pair of cages had a different length but a fixed diffusible surface area, so the surface area to volume ratio differed. Carrageenan was injected into half of the cages in each animal during one sampling period in a cross-over design. Samples from each cage and the bloodstream were obtained at 14-time points during two sampling periods. The concentration of carprofen was measured using LC–MS/MS and the results were modeled using nonlinear mixed-effects techniques. Prostaglandin metabolites were also measured and the change over time was analyzed using linear mixed effect modeling. Results: The presence of carrageenan within an animal changed the systemic pharmacokinetics of carprofen. The rate of drug movement into and out of the tissue cages varied with the surface area to volume ratio. The concentration time curve for prostaglandin metabolites changed with cage size. Conclusion: The surface area volume ratio of tissue cages will influence the calculated pharmacokinetic parameters and may affect calculated pharmacodynamics, thus, it is an important factor to consider when using tissue cage data for dosing regimes

Synthesis, Characterization and Application of Mayenite

The mineral mayenite (12CaO•7Al2O3, C12A7), possesses a unique cage structure which allows the entrapment of anions due to the positive charge of the cage. The most abundant form of this mineral is C12A7:O2- which exhibits high oxygen conductivity. However, the oxygen can be removed from the cage by reduction and other anions such as OH-, H-, Cl-, and even e- can be substituted in the cage. When electrons act as the anion in the cage, the material is classified as an electride. Mayenite electride shows promising properties such as metallic-like conduction and is a room temperature stable inorganic electride. The cages don’t necessarily need to be occupied by just one anion. It is possible to have a mixture of anions of different species in the cages of mayenite. Through mixed anions present in the cages, mixed conductivity becomes possible. With H- ions and electrons inhabiting the cages of mayenite, it is theoretically possible to have hydrogen permeate through the cages. This allows the material mayenite to be used as a hydrogen permeable membrane. Other applications of mayenite include catalysts for ammonia formation, as well as an energy material for the cathode and electrolyte of a solid oxide fuel cell. To have a hydrogen permeable membrane, the membrane should be fully dense with as many charge carriers as possible to manifest high permeability without allowing molecules to diffuse or permeate through the membrane. This work focuses on the synthesis of mayenite with mixed conductivity to act as a hydrogen permeable membrane. Different dopants were tested such as doping a thin membrane with iron to allow the membrane to be fully dense. Silicon was also investigated as a dopant to replace aluminum sites as to create cages with higher positive charges with a goal of creating a doped mayenite with higher electron densities. Characterization was completed to show that the structure remained when doping, and that doping with silicon did indeed increase the electron density. Work was done to investigate the permeability of hydrogen through a thin membrane of mayenite