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.     

Families of prudent self-avoiding walks

A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that have been counted so far in that they can wind around their starting point.Their enumeration was first addressed by Préa in 1997. He defined 4 classes of prudent walks, of increasing generality, and wrote a system of recurrence relations for each of them. However, these relations involve more and more parameters as the generality of the class increases.The first class actually consists of partially directed walks, and its generating function is well known to be rational. The second class was proved to have an algebraic (quadratic) generating function by Duchi (2005). Here, we solve exactly the third class, which turns out to be much more complex: its generating function is not algebraic, nor even D-finite.The fourth class—general prudent walks—is the only isotropic one, and still defeats us. However, we design an isotropic family of prudent walks on the triangular lattice, which we count exactly. Again, the generating function is proved to be non-D-finite.We also study the asymptotic properties of these classes of walks, with the (somewhat disappointing) conclusion that their endpoint moves away from the origin at a positive speed. This is confirmed visually by the random generation procedures we have designed.     

Study of beta-cyclodextrin/fluorinated trimethyl ammonium bromide surfactant inclusion complex by fluorinated surfactant ion selective electrode

The construction and performance of a liquid membrane electrode responsive to N-(1,1,2,2-tetrahydroperfluorooctyl)-N,N,N-trimethylammonium bromide (FTABr) and its use for the study of β-cyclodextrin/fluorinated surfactant inclusion complex is described. The electrode is based on the use of tetrahydroperfluorooctyltrimethylammonium-tetraphenylborate ion pair as electro active material in polyvinyl chloride (PVC) matrix plasticized using 2-Nitrophenyl octyl ether (NPOE). The electrode exhibits a fast, stable, reproducible and “Nernstian” response (59 ± 2 mV) for FTABr over the concentration range of 10⁻⁵ to 2 × 10⁻³ mol L⁻¹ at 298 K. The lowest detection limit is 2 × 10⁻⁶ mol L⁻¹ and the response time is around 20-30 s. The validity of the electrode, for detection of fluorinated surfactant ions and hence to carry out electrochemical measurements to study micellization of fluorinated surfactant, is verified by comparing the critical micelle concentration (cmc) value of FTABr obtained by using the electrode, with that obtained by surface tension measurements. Association constant K for β-cyclodextrin/FTABr complex is evaluated from the potentiometric measurements carried out using this electrode and is observed to be ∼1.26 × 10⁵. The results suggest that β-cyclodextrin forms an equimolar association complex with the FTA⁺ surfactant ion.     

Z‐Shaped Pyrrolo[3,2‐b]pyrroles and Their Transformation into π‐Expanded Indolo[3,2‐b]indoles

Sterically hindered 1,4‐dihydropyrrolo[3,2‐b]pyrroles possessing ortho‐(arylethynyl)phenyl substituents at positions‐2 and ‐5 were efficiently synthesized through a sila‐Sonogashira reaction. These unique Z‐shaped dyes showed relatively strong fluorescence in solution. Detailed optimization revealed that, in the presence of InCl₃, these alkynes readily undergo an intramolecular double cyclization to give hexacyclic products bearing an indolo[3,2‐b]indole skeleton in remarkable yields. Steady‐state UV–visible spectroscopy revealed that upon photoexcitation, the prepared Z‐shaped alkynes undergo mostly radiative relaxation leading to high fluorescence quantum yields. In the case of 7,14‐dihydrobenzo[g]benzo[6,7]indolo[3,2‐b]indoles, we believe that the substantial planarization of geometry in the excited state, is the underlying reason for the observed large Stokes shifts. The presence of additional electron‐withdrawing groups makes it possible to further alter the photophysical properties. The two‐photon absorption cross‐section values of both families of dyes were found to be modest and the nature of the excited state responsible for two‐photon absorption appeared to be strongly affected by the presence of peripheral groups. Serendipitous synthesis of unusual double‐Z‐shaped alkyne by Sonogashira and Glaser coupling is also reported.     

Two‐step Synthesis of New γ‐Lactones via Cyclization of 7‐Chloro‐2‐(methoxycarbonyl)‐4‐6‐dimethylocta‐(2E,4E,6E)‐trienoic acid

A new rapid synthesis of γ‐lactones, cis fused with a cyclopentenic ring by thermal cyclization of 7‐chloro‐2‐(methoxycarbonyl)‐4‐6‐dimethylocta‐7‐phenyl (or methyl) (2E,4E,6E)‐trienoic acids was reported. The key step implicates an intramolecular cyclization to a cyclopentenyl cation, according to an electrocyclic π_2s + π_2a conrotatory process, published in a recent paper (from the corresponding diacids). We have investigated the thermal behavior of the corresponding half‐esters since; if the cyclization obeys to the proposed mechanism, the diacids, half‐esters must also cyclize in a similar manner. Saponification of these led to γ‐dilactones via intermediary cyclopropanes. Mechanistic pathways were investigated.     

Membrane electrodes sensitive to doubly charged surfactants. Application to a cationic gemini surfactant

The response of a membrane electrode is not always identical to that of a redox electrode. Indeed, in the case of membrane electrode the response is not due to a redox equilibrium but to a cross-membrane potential. So, the membrane electrode's response depends mainly on the carrier system and the nature of the membrane. The properties of the membrane can favour several reactions giving rise to different ionic species diffusing in the membrane. The expression of the cross-membrane potential thus depends on the number and quantities of these ionic species. To illustrate this, we established the equations for the case of a two-charge cation detected by a univalent charged carrier. We show that the Nernstian response is not applicable to membrane electrodes. This approach allowed us to interpret results obtained with a cationic gemini surfactant-selective electrode prepared in the laboratory. To prove the well working of this electrode, we determined the critical micelle concentration in water and several NaBr solutions (0.004, 0.006, 0.01 and 0.02 M) from which the counterion binding has been determined.     

O- versus F-protonation in (CF3CF2)2O and CF3OCF(CF3)2: a preliminary theoretical study

The relative modifications induced in the structure of perfluorodiethyl ether (CF₃CF₂)₂O and perfluoroisopropyl methyl ether CF₃OCF(CF₃)₂ by oxygen and fluorine protonation are studied at the RHF level with the 3–21G basis and correlated with their proton affinities and dissociation energies.     

Reaktion von Phenyldiazomethan mit 1,3-Thiazol-5(4H)-thionen: Basenkatalysierte Ring-Öffnung des Primäradduktes

Reaction of Phenyldiazomethane with 1,3-Thiazole-5(4H)-thiones: Base-Catalyzed Ring Opening of the Primary Adduct Reaction of 1,3-thiazole-5(4H)-thiones 1 and phenyldiazomethane ( 2a ) in toluene at room temperature yields the thiiranes trans- and cis-1,4-dithia-6-azaspiro[2.4]hept-5-enes (trans- and cis- 4 ; Scheme 2). With Ph₃P in THF at 70°, these thiiranes are transformed stereospecifically into (E)- and (Z)-5-benzylidene-4,5-dihydro-1,3-thiazoles 5 , respectively. In the presence of DBU, 1 and 2a react to give 1,3,4-thiadiazole derivatives 6 or 7 via base-catalyzed ring opening of the primary cycloadduct (Scheme 3). In the case of 2-(alkylthio)-substituted 1,3-thiazole-5(4H)-thiones 1c and 1d , this ring opening proceeds by elimination of the corresponding alkylthiolate, yielding isothiocyanate 7 . The structures of (Z)- 5c and 6b have been established by X-ray crystallography.