Phosphorus-based nanothermites: A new generation of energetic materials

Thermites are energetic materials that are classically made of a transition metal oxide mixed with a reducing metal. Contrary to explosives, thermites do not detonate because their combustion is relatively slow and their reaction by-products are often solid or liquid. The use of nanoparticles to prepare superthermites is very promising. The dramatic changes observed in their reactivity were reported by numerous recent papers dealing with the use of aluminium as fuel.Red phosphorus is widely used in pyrotechnic devices. Highly explosive compositions are classically obtained by mixing this substance with strong oxidizers such as oxygenated potassium salts (chlorate, nitrate). But to our knowledge, the idea to prepare P-nanothermites with metallic oxide nanoparticles was never reported before. In order to illustrate this new concept of energetic formulations, P-nanothermites were prepared from nickel oxide (NiO), iron oxide (Fe₂O₃), and copper oxide (CuO) nanopowders. The reactivity of these compositions was studied by thermogravimetric analysis, impact and friction tests, electrostatic discharge and high-speed cinematography. P-nanothermites are very insensitive to thermal and impact stress. Their combustion rates strongly depend on the nature of the oxide (NiO <Fe₂O₃?CuO). The SEM observation of the microstructure of the residues produced by the combustion clearly indicates that they were formed by the solidification of molten phases. In other words, the energy released by the combustion of P-nanothermites provokes the melting of the reaction products. The temperatures reached are thus high enough to cause the gasification of phosphoric anhydride produced by the combustion. For this reason, P-nanothermites can be considered gas-generating materials.     

Optical design of a freeform TIR lens for LED streetlight

Secondary optics is a critical component determining the output efficiency and light distribution of the LED streetlight. A good roadway illumination requires the LED streetlight have a rectangular light pattern just cover the roadway and without excess spill light creeping into yards and shining into windows of neighbor residents. The adoption of the unsymmetrical freeform optics with different light distributions along X and Y directions is necessary. The whole LED streetlight can be constructed if only mounts these LED modules on the planar PCB plate. The mechanism, thermal management, and the power control electronics of the LED streetlight become very simple. In this paper, an optical design approach of a freeform TIR (total internal reflection) lens for the LED streetlight is investigated. With these freeform lenses, high output efficiency, even light distribution, and batwing far field beam angle distribution can be achieved.     

A randomized embedding algorithm for trees

In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a “self-avoiding tree-indexed random walk“. The order of the tree T can be as large as a constant fraction of the order of the graph G, and the maximum degree of T can be close to the minimum degree of G. We show that our algorithm works in a variety of interesting settings. For example, we prove that any graph of minimum degree d without 4-cycles contains every tree of order εd ² and maximum degree at most d-2εd-2. As there exist d-regular graphs without 4-cycles and with O(d ²) vertices, this result is optimal up to constant factors. We prove similar nearly tight results for graphs of given girth and graphs with no complete bipartite subgraph K _s,t .     

Hamiltonicity thresholds in Achlioptas processes

In this article, we analyze the appearance of a Hamilton cycle in the following random process. The process starts with an empty graph on nlabeled vertices. At each round we are presented with K = K(n) edges, chosen uniformly at random from the missing ones, and are asked to add one of them to the current graph. The goal is to create a Hamilton cycle as soon as possible. We show that this problem has three regimes, depending on the value of K. For K = o(log n), the threshold for Hamiltonicity is n log n, i.e., typically we can construct a Hamilton cycle K times faster that in the usual random graph process. When K = ω(log n) we can essentially waste almost no edges, and create a Hamilton cycle in n + o(n) rounds with high probability. Finally, in the intermediate regime where K = Θ(log n), the threshold has order nand we obtain upper and lower bounds that differ by a multiplicative factor of 3. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

S‐Functionalized Cysteine: Powerful Ligands for the Labelling of Bioactive Molecules with Triaquatricarbonyltechnetium‐99m(1+) ([99mTc(OH2)3(CO)3]+)

S‐Alkylated cysteines are used as efficient tridentate N,O,S‐donor‐atom ligands for the fac‐[M(CO)₃]⁺ moiety (M=^99mTc or Re). Reaction of (Et₄N)₂[ReBr₃(CO)₃] ( 3 ) with the model S‐benzyl‐L ‐cysteine ( 2 ) leads to the formation of [Re( 2′ )(CO)₃] ( 4 ) as the exclusive product ( 2′ =C‐terminal anion of 2 ). The tridentate nature of the alkylated cysteine in 4 was established by X‐ray crystallography. Compound 2 reacts with [^99mTc(OH₂)₃(CO)₃]⁺ under mild conditions (10⁻⁴ M , 50°, 30 min) to afford [^99mTc( 2′ )(CO)₃] ( 5 ) and represents, therefore, an efficient chelator for the labelling of biomolecules. L ‐Cysteine, S‐alkylated with a 3‐aminopropyl group (→ 7 ), was conjugated via a peptide coupling sequence with Coα‐[α‐(5,6‐dimethyl‐1H‐benzimidazolyl)]‐Coβ‐cyanocobamic b‐acid ( 6 ), the b‐acid of cyanocob(III)alamin (vitamin B₁₂) (Scheme 3). More convenient was a one‐pot procedure with a derivative of vitamin B₁₂ comprising a free amine group at the b‐position. This amine 15 was treated with NHS (N‐hydroxysuccinimide)‐activated 1‐iodoacetic acid 14 to introduce an I‐substituent in vitamin B₁₂. Subsequent addition of unprotected L ‐cysteine resulted in nucleophilic displacement of the I‐atom by the S‐substituent, affording the vitamin B₁₂ alkylated cysteine fragment 17 (Scheme 4). The procedure was quantitative and did not require purification of intermediates. Both cobalamin–cysteine conjugates could be efficiently labelled with [^99mTc(OH₂)₃(CO)₃]⁺ ( 1 ) under conditions identical to those of the model complex 5 . Biodistribution studies of the cobalamin conjugates in mice bearing B10‐F16 melanoma tumors showed a tumor uptake of 8.1±0.6% and 4.4±0.5% injected dose per gram of tumor tissue after 4 h and 24 h, respectively (Table 1).     

N(epsilon) functionalization of metal and organic protected L-histidine for a highly efficient,direct labeling of biomolecules with [Tc(OH2)3(CO)3]+

Two different pathways for the introduction of an acetyl group at N(epsilon ) in a N(alpha), N(delta), and -COO protected histidine to afford N(epsilon)-(CH(2)COOH)-histidine derivative 7 b are presented. The purpose of this study is the coupling of 7 b to amino groups in bioactive molecules such as peptides. After full deprotection of such a bioconjugate, histidine provides three coordination sites which efficiently coordinate to [(99m)Tc(OH(2))(3)(CO)(3)](+) or [Re(OH(2))(3)(CO)(3)](+) in a facial geometry. This allows the development of novel radiopharmaceuticals. Selective derivatization at the N(epsilon) position has conveniently been achieved by concomitant protection of N(alpha) and N(delta) with a carbonyl group forming a six-membered urea. Cyclic urea ring opening with Fm-OH, coupling of phenylalanine as a model to 7 b through its primary amine and removing of all protecting groups in one step gave a histidine derivative of phenylalanine which could be labeled at 10(-5) M with (99m)Tc in very high yield and even in about 50 % yield at 10(-6) M. The Xray structure of a complex with [Re(CO)(3)](+) in which anilin is coupled to 7 b confirms the facial arrangement of histidine. A second pathway applies directly the [Re(CO)(3)](+) moiety as a protecting group. This is one of the rare examples in which a metal fragment is used as a protecting group for organic functionalities. The coordination to histidine protects the N(alpha), N(delta) and COO group in one single step, subsequent alkylation with BrCH(2)COOH(R) at N(epsilon), coupling to phenylalanine and oxidative deprotection of [Re(CO)(3)](+) to [ReO(4)](-) gave the corresponding bioconjugate in which histidine is coupled to phenylalanine through an acetylamide at N(epsilon). Both methods offer convenient pathways to introduce histidine in a biomolecule under retention of its three coordination sites. The procedures are adaptable to any biomolecule with pendant amines and allow the development of novel radiopharmaceuticals or inversed peptides.     

Acceleration of Correlation-corrected Vibrational Self-consistent Field Calculation Times for Large Polyatomic Molecules

Acceleration of the correlation-corrected Vibrational self-consistent field (CC-VSCF) method for anharmonic calculations of vibrational states of polyatomic molecules is described. The acceleration assumes pairwise additive interactions between different normal modes, and employs orthogonality of the single-mode vibrational wavefunctions. This greatly reduces the effort in computing correlation effects between different vibrational modes, which is treated by second order perturbation theory in CC-VSCF. The acceleration can improve the scaling of the overall computational effort from N ⁶ to N ⁴, where N is the number of vibrational modes. Sample calculation times, using semi-empirical potential surfaces (PM3), are given for a series of glycine peptides. Large computational acceleration, and significant reduction of the scaling of the effort with system size, is found and discussed.     

Exact and approximate solutions to the one-center McMurchie–Davidson tree-search problem

We have attempted to optimize the cost (the total number of floating-point operations required) of using the McMurchie–Davidson R_NLMj recurrence relation. Rigorous solutions of the tree-search problem inherent in the cost minimization are given for total angular momentum L ≤ 7. For L ≥ 8, the rigorous search algorithm is prohibitively expensive, and we propose an approximate algorithm that generates highly optimized trees. Cost comparisons demonstrate that the present scheme is consistently superior to two others currently in use.