Computing the non-linear anomalous diffusion equation from first principles

We investigate asymptotically the occurrence of anomalous diffusion and its associated family of statistical evolution equations. Starting from a non-Markovian process à la Langevin we show that the mean probability distribution of the displacement of a particle follows a generalized non-linear Fokker-Planck equation. Thus we show that the anomalous behavior can be linked to a fast fluctuation process with memory from a microscopic dynamics level, and slow fluctuations of the dissipative variable. The general results can be applied to a wide range of physical systems that present a departure from the Brownian regime.     

Temperature‐dependent Raman scattering studies of the geometrically frustrated pyrochlores Dy2Ti2O7, Gd2Ti2O7 and Er2Ti2O7

The temperature‐dependent Raman studies of A₂Ti₂O₇(A = Dy, Er, Gd) were performed on single crystals and polycrystalline samples in the 4.2–295 K temperature range. The Raman spectra showed softening of the majority of phonon modes upon cooling in the whole temperature range studied and large decrease of linewidths. These changes have been analyzed in terms of strong third‐order phonon–phonon anharmonic interactions. Moreover, the 312 and 330 cm⁻¹ modes of Er₂Ti₂O₇(Gd₂Ti₂O₇) showed hardening upon cooling down to about 130 K (100 K) and then anomalous softening below this temperature. The observed anomalous behavior of the Raman modes indicates that some important changes occur in these materials at low temperatures. However, the origin of this behavior is still not clear. Copyright © 2008 John Wiley & Sons, Ltd.     

Description and interpretation of the bracts epidermis of Gramineae (Poaceae) with rotated image with maximum average power spectrum (RIMAPS) technique

During the last few years, RIMAPS technique has been used to characterize the micro-relief of metallic surfaces and recently also applied to biological surfaces. RIMAPS is an image analysis technique which uses the rotation of an image and calculates its average power spectrum. Here, it is presented as a tool for describing the morphology of the trichodium net found in some grasses, which is developed on the epidermal cells of the lemma. Three different species of grasses (herbarium samples) are analyzed: Podagrostis aequivalvis (Trin.) Scribn. & Merr., Bromidium hygrometricum (Nees) Nees & Meyen and Bromidium ramboi (Parodi) Rúgolo. Simple schemes representing the real microstructure of the lemma are proposed and studied. RIMAPS spectra of both the schemes and the real microstructures are compared. These results allow inferring how similar the proposed geometrical schemes are to the real microstructures. Each geometrical pattern could be used as a reference for classifying other species. Finally, this kind of analysis is used to determine the morphology of the trichodium net of Agrostis breviculmis Hitchc. As the dried sample had shrunk and the microstructure was not clear, two kinds of morphology are proposed for the trichodium net of Agrostis L., one elliptical and the other rectilinear, the former being the most suitable.     

Transition-Metal-Free Multiple Functionalization of Piperidines to 4-Substituted and 3,4-Disubstituted 2-Piperidinones

Remote and multiple functionalization of piperidines without the use of transition-metal catalysts and elaborate directing groups is one of the major challenges in organic synthesis. Herein is reported an unprecedented two-step protocol that enables the multiple functionalization of piperidines to either 4-substituted or trans-3,4-disubstituted 2-piperidones. First, by exploiting the duality of TEMPO reactivity, which under oxidative and thermal conditions fluctuates between cationic and persistent-radical form, a novel multiple C(sp³)-H oxidation of piperidines to α,β-unsaturated 2-piperidones was developed. Second, the intrinsic low reactivity of the unsaturated piperidones toward conjugated Grignard additions was overcome by using trimethylsilyl chloride (TMSCl) as Lewis acid. Subsequently, conjugated Grignard addition/electrophilic trapping protocol provided substituted 2-piperidone intermediates, some of which were then transformed into pharmaceutical alkaloids.     

Fast Exfoliation and Functionalisation of Two‐Dimensional Crystalline Carbon Nitride by Framework Charging

Two‐dimensional (2D) layered graphitic carbon nitride (gCN) nanosheets offer intriguing electronic and chemical properties. However, the exfoliation and functionalisation of gCN for specific applications remain challenging. We report a scalable one‐pot reductive method to produce solutions of single‐ and few‐layer 2D gCN nanosheets with excellent stability in a high mass yield (35 %) from polytriazine imide. High‐resolution imaging confirmed the intact crystalline structure and identified an AB stacking for gCN layers. The charge allows deliberate organic functionalisation of dissolved gCN, providing a general route to adjust their properties.     

Uncatalyzed, anti-Michael addition of amines to β-nitroacrylates: practical, eco-friendly synthesis of β-nitro-α-amino esters

A variety of primary and secondary amines give the conjugate reaction with β-nitroacrylates, via an anti-Michael addition, without any catalyst and/or solvent, allowing good yields of β-nitro-α-amino esters.     

Osmotic coefficients of aqueous solutions of four ionic liquids at T = (313.15 and 333.15) K

Measurements of osmotic coefficients of BmimCl (1-butyl-3-methylimidazolium chloride), HmimCl (1-hexyl-3-methylimidazolium chloride), MmimMeSO₄ (1,3-dimethylimidazolium methylsulfate), and BmimMeSO₄ (1-butyl-3-methylimidazolium methylsulfate) with water at T = (313.15 and 333.15) K are reported in this work. Vapour pressure and activity data of all the studied binary systems are obtained from experimental data. The osmotic coefficients data are correlated using the extended Pitzer model of Archer and the modified NRTL (MNRTL) model and standard deviations obtained with both models are given too. The parameters obtained with the extended Pitzer model of Archer are used to calculate the mean molal activity coefficients.     

Manganese cationic pyrazolylamidino complexes

The reactions of fac-[MnBr(CO)₃(NHC(CH₃)pz^∗-κ²N,N)] (pz^∗ = pz, dmpz; pzH = pyrazole; dmpzH = 3,5-dimethylpyrazole) with wet AgBF₄ in a 1:1 ratio lead to the cationic pyrazolylamidino complexes fac-[Mn(OH₂)(CO)₃(NHC(CH₃)pz^∗-κ²N,N)]BF₄. The aquo ligand is readily substituted by 2,6-xylylisocyanide (CNXyl) to give fac-[Mn(CNXyl)(CO)₃(NHC(CH₃)pz^∗-κ²N,N)]BF₄. The pyrazole complexes fac-[Mn(pz^∗H)(CO)₃(NHC(CH₃)pz^∗-κ²N,N)]BF₄ are obtained by treating fac-[MnBr(CO)₃(NCMe)₂] with AgBF₄ and then with pyrazole (pzH or dmpzH), in a 1:1:2 ratio. A similar reaction using 1:1:1 ratio and AgClO₄ leads to the acetonitrile complexes fac-[Mn(NCMe)(CO)₃(NHC(CH₃)pz^∗-κ²N,N)]ClO₄. The X-ray structures of the complexes show moderate hydrogen bonds interactions between the N-bond hydrogen of the pyrazolylamidino ligand and the anion. In the aquo complex, one of the hydrogens of the coordinated water molecule is also involved in a hydrogen bond.     

Structural Diversity in Alkali Metal and Alkali Metal Magnesiate Chemistry of the Bulky 2,6‐Diisopropyl‐N‐(trimethylsilyl)anilino Ligand

Bulky amido ligands are precious in s‐block chemistry, since they can implant complementary strong basic and weak nucleophilic properties within compounds. Recent work has shown the pivotal importance of the base structure with enhancement of basicity and extraordinary regioselectivities possible for cyclic alkali metal magnesiates containing mixed n‐butyl/amido ligand sets. This work advances alkali metal and alkali metal magnesiate chemistry of the bulky arylsilyl amido ligand [N(SiMe₃)(Dipp)]^? (Dipp=2,6‐iPr₂‐C₆H₃). Infinite chain structures of the parent sodium and potassium amides are disclosed, adding to the few known crystallographically characterised unsolvated s‐block metal amides. Solvation by N,N,N′,N′′,N′′‐pentamethyldiethylenetriamine (PMDETA) or N,N,N′,N′‐tetramethylethylenediamine (TMEDA) gives molecular variants of the lithium and sodium amides; whereas for potassium, PMDETA gives a molecular structure, TMEDA affords a novel, hemi‐solvated infinite chain. Crystal structures of the first magnesiate examples of this amide in [MMg{N(SiMe₃)(Dipp)}₂(μ‐nBu)]_∞ (M=Na or K) are also revealed, though these breakdown to their homometallic components in donor solvents as revealed through NMR and DOSY studies.     

Chromogenic signaling of hydrogen carbonate anion with pyrylium-containing polymers

Polymeric films containing pyrylium derivatives showing a selective color modulation from yellow to red in the presence of the poorly coordinating hydrogen carbonate anion in water at neutral pH have been developed.