Coupled Sensitizer–Catalyst Dyads: Electron‐Transfer Reactions in a Perylene–Polyoxometalate Conjugate

Ultrafast discharge of a single‐electron capacitor: A variety of intramolecular electron‐transfer reactions are apparent for polyoxometalates functionalized with covalently attached perylene monoimide chromophores, but these are restricted to single‐electron events. (et=electron transfer, cr=charge recombination, csr=charge‐shift reaction, PER=perylene, POM=polyoxometalate).

     

Crystal Memory near Discontinuous Triacylglycerol Phase Transitions: Models,Metastable Regimes,and Critical Points

It is proposed that “crystal memory”, observed in a discontinuous solid-liquid phase transition of saturated triacylglycerol (TAG) molecules, is due to the coexistence of solid TAG crystalline phases and a liquid TAG phase, in a superheated metastable regime. Such a coexistence has been detected. Solid crystals can act as heterogeneous nuclei onto which molecules can condense as the temperature is lowered. We outlined a mathematical model, with a single phase transition, that shows how the time-temperature observations can be explained, makes predictions, and relates them to recent experimental data. A modified Vogel-Fulcher-Tammann (VFT) equation is used to predict time-temperature relations for the observation of “crystal memory” and to show boundaries beyond which “crystal memory” is not observed. A plot of the lifetime of a metastable state versus temperature, using the modified VFT equation, agrees with recent time-temperature data. The model can be falsified through its predictions: the model possesses a critical point and we outline a procedure describing how it could be observed by changing the hydrocarbon chain length. We make predictions about how thermodynamic functions will change as the critical point is reached and as the system enters a crossover regime. The model predicts that the phenomenon of “crystal memory” will not be observed unless the system is cooled from a superheated metastable regime associated with a discontinuous phase transition.     

Toward the comparison of rare earth element and actinide behavior in materials: a computational study of Ce- and U-bearing britholites

We present a computational investigation into the nature of bonds formed by f-elements in materials. The paper presents an example of the incorporation of rare earth elements (REE) and actinides in minerals derived from fluorapatite: Ca(10)(PO(4))(6)F(2). These minerals, called britholites, allow many substitutions on all three Ca, P, and F sites and are considered as potential host phases for radioactive elements separated from nuclear waste. REE and actinides have very similar physical and chemical properties, but REE are not radioactive and much more easily handled. REE are, therefore, very often used as a surrogate for actinides in experimental studies. The representative elements of rare earths and actinides chosen for this first investigation are cerium and uranium, respectively. We have studied all the various configurations of Ca(9)X(PO(4))(6)(-)(y)()(SiO(4))(y)()F(2), where X stands for Ce(3+), Ce(4+), U(3+), and U(4+), and y is equal to 1 and 2 for three-time and four-time charged cations, respectively. Calculations have been performed within the density functional theory (DFT) framework according to the computation scheme determined in a previous study. The analysis of the energies of the various configurations shows that the incorporation of all the cations considered stabilizes the apatitic structure. This stabilization, however, is greater for four-time charged cations than for three-time charged ones, which shows that Ce and U are both preferentially substituted in the +IV oxidation state. In addition, the substitution in one of the two cationic sites of the apatitic structure is always more favorable. Then, the geometry analysis shows a larger decrease in size of this cationic site for U than for Ce, as well as different volume variations for Ce and U substitutions in the two cationic sites. This cannot be explained by steric effects alone. Finally, the electronic density analysis yields three essential results: U and Ce form significantly covalent bonds, U forms bonds more covalent than Ce, and finally four-time charged cations form more covalent bonds than three-time charged ones. The comparison of these results with the formation enthalpies of the various phases shows a positive correlation between the covalence degree of the bonds formed by the f-element and the stability of the structure. In addition, our results prove that Ce- and U-bearing britholites exhibit very similar energetic, structural, and electronic properties. Ce, therefore, appears to be a good simulant for U.     

On the Characterization of Expansion Maps for Self-Affine Tilings

We consider self-affine tilings in ℝ ⁿ with expansion matrix φ and address the question which matrices φ can arise this way. In one dimension, λ is an expansion factor of a self-affine tiling if and only if |λ| is a Perron number, by a result of Lind. In two dimensions, when φ is a similarity, we can speak of a complex expansion factor, and there is an analogous necessary condition, due to Thurston: if a complex λ is an expansion factor of a self-similar tiling, then it is a complex Perron number. We establish a necessary condition for φ to be an expansion matrix for any n, assuming only that φ is diagonalizable over ℂ. We conjecture that this condition on φ is also sufficient for the existence of a self-affine tiling.     

Opening crystallography

Structural Chemistry - This essay surveys results of the past 4 years, starting with a week-long workshop on “Soft Packings, Nested Clusters, and Condensed Matter” held in...     

Exact thought in a demented time: Karl menger and his viennese mathematical colloquium

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Spectral shape discrimination by hearing-impaired and normal-hearing listeners

The ability to discriminate between sounds with different spectral shapes was evaluated for normal-hearing and hearing-impaired listeners. Listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level. In one condition, the standard stimulus was the sum of six equal-amplitude tones (equal-SPL), and in another the standard stimulus was the sum of six tones at equal sensation levels re: audiometric thresholds for individual subjects (equal-SL). Spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation. Sensitivity was similar in all conditions for normal-hearing and hearing-impaired listeners. The presence of perturbation and equal-SL components increased thresholds for both groups, but only small differences in weighting strategy were measured between the groups depending on whether the equal-SPL or equal-SL condition was tested. The average data suggest that normal-hearing listeners may rely more on the central components of the spectrum whereas hearing-impaired listeners may have been more likely to use the edges. However, individual weighting functions were quite variable, especially for the HI listeners, perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss. Differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights, such as internal noise or difficulty encoding a reference stimulus, also may dominate performance.