Algebraic Numbers Close to 1 in Non-Archimedean Metrics

Let 1 be an algebraic number with relatively small height. Recently, many authors, including Amoroso, Dubickas, Mignotte and Waldschmidt, stated sharp lower bounds for the quantity | – 1|. Here, we provide a p-adic analogue of their results. For instance, we give an upper bound for the absolute value of the norm of – 1, and we show that our estimate is rather sharp in terms of the degree of . Further, we discuss a generalization in several variables of our result.     

Increasing the Efficiency of Organic Dye‐Sensitized Solar Cells over 10.3% Using Locally Ordered Inverse Opal Nanostructures in the Photoelectrode

3D inverse opal (3D‐IO) oxides are very appealing nanostructures to be integrated into the photoelectrodes of dye‐sensitized solar cells (DSSCs). Due to their periodic interconnected pore network with a high pore volume fraction, they facilitate electrolyte infiltration and enhance light scattering. Nonetheless, preparing 3D‐IO structures directly on nonflat DSSC electrodes is challenging. Herein, 3D‐IO TiO₂ structures are prepared by templating with self‐assembled polymethyl methacrylate spheres on glass substrates, impregnation with a mixed TiO₂:SiO₂ precursor and calcination. The specific surface increases from 20.9 to 30.7 m² g^?1 after SiO₂ removal via etching, which leads to the formation of mesopores. The obtained nanostructures are scraped from the substrate, processed as a paste, and deposited on photoelectrodes containing a mesoporous TiO₂ layer. This procedure maintains locally the 3D‐IO order. When sensitized with the novel benzothiadiazole dye YKP‐88, DSSCs containing the modified photoelectrodes exhibit an efficiency of 10.35% versus 9.26% for the same devices with conventional photoelectrodes. Similarly, using the ruthenium dye N719 as sensitizer an efficiency increase from 5.31% to 6.23% is obtained. These improvements originate mainly from an increase in the photocurrent density, which is attributed to an enhanced dye loading obtained with the mesoporous 3D‐IO structures due to SiO₂ removal.     

Assembly and Characterizations of Bifunctional Fluorescent and Magnetic Microneedles With One Decade Length Tunability

This report presents the fabrication of bifunctional magnetic and fluorescent microneedles (µNDs) made of a ternary mixture of magnetic nanoparticles (NPs), quantum dots (QDs), and polyelectrolyte. The assembly relies on the electrostatic complexation of negatively charged NPs with positively charged polymer strands and is controlled by the charge ratio between the nanoparticle building blocks and the polymer mortar. The resulting 1D objects can be actuated using an external magnetic field and can be imaged using fluorescence microscopy, thanks to the fluorescent and superparamagnetic properties inherited from their NP constituents. Using a combination of core and surface characterizations and a state‐of‐the‐art image analysis algorithm, the dependence of the brightness and length on the ternary composition is thoroughly investigated. In particular, statistics on hundreds of µNDs with a range of compositions show that the µNDs have a log‐lormal length distribution and that their mean length can be robustly tuned in the 5–50 µm range to match the relevant length scales of various applications in micromixing, bioassays or biomechanics.     

Synthesis of new perylene imide dyes and their photovoltaic performances in nanocrystalline TiO2 dye-sensitized solar cells

Eight novel perylene imide derivatives were synthesized to determine the effect of the nature of electron donating substituents on the perylene core (ether or N-amino), the position of the carboxylic acid anchoring group and the presence of a fused benzimidazole moiety on the performances of dye-sensitized solar cells. The photovoltaic efficiency under AM1.5 of these new dyes, although not optimized, ranges from 0.2% until 2.3%. We note the importance of the position-anchoring group, which controls the electron injection efficiency. With respect to the excited-state electron donor strength, four O-aryl substituents at the bay position lead to similar effect as two N-piperidinyl groups but with a lower propensity to aggregation and give slightly higher photovoltaic performance than the latter. The benzimidazole unit extends the absorbance of the perylene imide to longer wavelengths, but this effect is lower than introducing charge transfer transition with N-amino substituents. Overall, this work shows that perylene imide remains a promising molecular basis for the future design of new fully organic sensitizers for nanostructured TiO₂ solar cells.     

Modeling procyanidin self-association processes and understanding their micellar organization: a study by diffusion NMR and molecular mechanics

The colloidal behavior of eight synthetic procyanidins (three monomers, four dimers, and a trimer) has been investigated in water or in a winelike medium using DOSY NMR spectroscopy and molecular dynamics simulations. Different behavior was observed for monomers and oligomers. Monomers self-associate with a high affinity constant (37-53 M(-1)) to form micelles at low cmc (critical micelle concentration) values (1-5 g.L(-1)). These micelles undergo a time-dependent coalescence process to form hazes and precipitates. As for dimers and the trimer, self-association also occurs but with a lower affinity (approximately 6 M(-1)) and at higher cmc values (10-20 g.L(-1)) to form small micelles (<5 nm) that remain stable throughout the experiment. The presence of 10% ethanol does not significantly affect the self-association constant for monomers and oligomers but increases their cmc values by approximately 50% and decreases the micelle size by a factor 2. However, the presence of 20 mM NaCl appears to negate the effect of ethanol. This study helps to clarify the role of procyanidin monomers versus oligomers in wine turbidity and demonstrates that procyanidin oligomers are fully available to interact with saliva proteins.     

Gas‐Phase Infrared Spectroscopy of Substituted Cyanobutadiynes: Roles of the Bromine Atom and Methyl Group as Substituents

The IR spectra of 5‐bromo‐2,4‐pentadiynenitrile (Br?C≡C?C≡C?CN) and 2,4‐hexadiynenitrile (CH₃?C≡C?C≡C?CN), a compound of interstellar interest, have been recorded within the 4000–500 cm^?1 spectral region and calculated by means of high‐level ab initio and density functional calculations. Although the calculated structures of both compounds are rather similar, there are very subtle differences, mainly in the strength of the C≡C bond not directly bound to the substituent. These subtle bonding differences are reflected in small, but not negligible, differences in the electron density at the corresponding bond critical points, and, more importantly, are reflected in the IR spectra. Indeed, the IR spectrum for the bromine derivative presents two well‐differentiated strong bands around 2250 cm^?1, whereas for the methyl derivative both absorptions coalesce in a single band. These bands correspond in both cases to the coupling between C≡C and C≡N stretching displacements. A third, very weak, band also associated with C≡C and C≡N coupled stretches is observed for the bromine derivative, but not for the methyl one, owing to its extremely low intensity.     

Infrared and Raman Spectroscopy of Methylcyanodiacetylene (CH3C5N)

A spectroscopic study combining IR absorption and Raman scattering is presented for methylcyanodiacetylene (CH₃C₅N). Gas‐phase, cryogenic matrix‐isolated, and pure solid‐phase substance was analyzed. Out of 16 normal vibrational modes, 14 were directly observed. The analysis of the spectra was assisted by quantum chemical calculations of vibrational frequencies, IR absorption intensities, and Raman scattering activities at density functional theory and ab initio levels. Previous assignments of gas‐phase IR absorption bands were revisited and extended.     

Nuclear quantum effects on the thermal expansion coefficient of hexagonal boron nitride monolayer

This work examines the importance of vibrational delocalization on a basicthermomechanical property of a hexagonal boron nitride monolayer, namely its thermalexpansion coefficient (TEC). Using a recently parametrized bond-order potential of theTersoff type, the TEC was theoretically obtained from the thermal variations of thelattice parameter a(T) calculated using threedifferent methods: (i) the quasiharmonic approximation; (ii) its anharmonic improvementbased on self-consistent phonons; (iii) fully anharmonic Monte Carlo simulations possiblyenhanced within the path-integral framework to account for nuclear quantum effects. Theresults obtained with the three methods are generally consistent with one another and withother recently published data, and indicate that the TEC is negative at least up to ca.700 K, quantum mechanical effects leading to a significant expansion by about 50% relativeto the classical result. Comparison with experimental data on bulk hexagonal BN suggestssignificant differences, which originate from possible inaccuracies in the model that tendto underestimate the lattice parameter itself, and most likely from the 2D nature of themonolayer and the key contribution of out-of-plane modes. The effects of isotopic purityin the natural abundances of boron are found to be insignificant.     

Estimate of the vibrational contribution to the entropy change associated with the spin transition in the d4 systems [MnIII(pyrol)3tren] and [CrII(depe)2I2

The vibrational contribution to DeltaS of the low-spin ((3)T(1)) to high-spin ((5)E) spin transition in two 3d(4) octahedral systems [Mn(III)(pyrol)(3)tren] and [Cr(depe)(2)I(2)] have been estimated by means of DFT calculations (B3LYP/CEP-31G) of the vibrational normal-modes frequencies. The obtained value at the transition temperature for the Mn(iii) complex is DeltaS(vib)(44 K) = 6.3 J K(-1) mol(-1), which is comparable with the proposed Jahn-Teller contribution of R ln3 = 9.1 J K(-1) mol(-1) and which is approximately half of the experimentally determined 13.8 J K(-1) mol(-1). The corresponding value for the Cr(ii) complex is DeltaS(vib)(171.45 K) = 46.5 J K(-1) mol(-1), as compared to the experimental value of 39.45 J K(-1) mol(-1). The analysis of the vibrational normal modes reveals that for the d(4) systems under study, contrary to Fe(ii) d(6) systems, not all metal-ligand stretching vibrations make a contribution. For the Mn(iii) complex, the only vibration that contributes to DeltaS(vib) involve the nitrogens occupying the Jahn-Teller axis, while in the case of Cr(ii) the contributing vibrations involve the Cr-I bonds. Low-frequency modes due to ring vibrations, metal-ligand bending and movement of the molecule as a whole also contribute to the vibrational entropy associated with the spin transition.     

Dynamics and supramolecular organization of the 1D spin transition polymeric chain compound [Fe(NH2trz)3](NO3)2. Muon spin relaxation

The thermal spin transition that occurs in the polymeric chain compound [Fe(NH(2)trz)3](NO3)2 above room temperature has been investigated by zero-field muon spin relaxation (microSR) over the temperature range approximately 8-402 K. The depolarization curves are best described by a Lorentzian and a Gaussian line that represent fast and slow components, respectively. The spin transition is associated with a hysteresis loop of width DeltaT = 34 K (T1/2 upward arrow = 346 K and T1/2 downward arrow = 312 K) that has been delineated by the temperature variation of the initial asymmetry parameter, in good agreement with previously published magnetic measurements. Zero-field and applied field (20-2000 Oe) microSR measurements show the presence of diamagnetic muon species and paramagnetic muonium radical species (A = 753 +/- 77 MHz) over the entire temperature range. Fast dynamics have been revealed in the high-spin state of [Fe(NH(2)trz)3](NO3)2 with the presence of a Gaussian relaxation mode that is mostly due to the dipolar interaction with static nuclear moments. This situation, where the muonium radicals are totally decoupled and not able to sense paramagnetic fluctuations, implies that the high-spin dynamics fall outside the muon time scale. Insights to the origin of the cooperative effects associated with the spin transition of [Fe(NH(2)trz)3](NO3)2 through muon implantation are presented.