The Influence of the Symmetry of Identical Particles on Flight Times

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a ‘screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.     

Network Dynamics in Elemental Assimilation and Metabolism

Metabolism and physiology frequently follow non-linear rhythmic patterns which are reflected in concepts of homeostasis and circadian rhythms, yet few biomarkers are studied as dynamical systems. For instance, healthy human development depends on the assimilation and metabolism of essential elements, often accompanied by exposures to non-essential elements which may be toxic. In this study, we applied laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) to reconstruct longitudinal exposure profiles of essential and non-essential elements throughout prenatal and early post-natal development. We applied cross-recurrence quantification analysis (CRQA) to characterize dynamics involved in elemental integration, and to construct a graph-theory based analysis of elemental metabolism. Our findings show how exposure to lead, a well-characterized toxicant, perturbs the metabolism of essential elements. In particular, our findings indicate that high levels of lead exposure dysregulate global aspects of metabolic network connectivity. For example, the magnitude of each element’s degree was increased in children exposed to high lead levels. Similarly, high lead exposure yielded discrete effects on specific essential elements, particularly zinc and magnesium, which showed reduced network metrics compared to other elements. In sum, this approach presents a new, systems-based perspective on the dynamics involved in elemental metabolism during critical periods of human development.     

Dramatically Enhanced Fluorescence of Heteroaromatic Chromophores upon Insertion as Spacers into Oligo(triacetylene)s

In continuation of a previous study on the modulation of π‐electron conjugation of oligo(triacetylene)s by insertion of central hetero‐spacer fragments between two (E)‐hex‐3‐ene‐1,5‐diyne ((E)‐1,2‐diethynylethene, DEE) moieties (Fig. 1), a new series of trimeric hybrid oligomers ( 14 – 18 and 22 – 24 , Fig. 2) were prepared (Schemes 1–3). Spacers used were both electron‐deficient (quinoxaline‐based heterocycles, pyridazine) and electron‐rich (2,2′‐bithiophene, 9,9‐dioctyl‐9H‐fluorene) chromophores. With 19–21 (Scheme 4), a series of transition metal complexes was synthesized as potential precursors for nanoscale scaffolding based on both covalent acetylenic coupling and supramolecular assembly. The UV/VIS spectra (Fig. 3) revealed that the majority of spacers provided hetero‐trimers featuring extended π‐electron delocalization. The new hybrid chromophores show a dramatically enhanced fluorescence compared with the DEE dimer 13 and homo‐trimer 12 (Fig. 5). This increase in emission intensity appears as a general feature of these systems: even if the spacer molecule is non‐fluorescent, the corresponding hetero‐trimer may show a strong emission (Table 2). The redox properties of the new hybrid chromophores were determined by cyclic voltammetry (CV) and rotating‐disk voltammetry (RDV) (Table 3 and Fig. 5). In each case, the first one‐electron reduction step in the hetero‐trimers appeared anodically shifted compared with DEE dimer 13 and homo‐trimer 12 . With larger spacer chromophore extending into two dimensions (as in 14 – 18 , Fig. 2), the anodic shift (by 240–490 mV, Table 3) seems to originate from inductive effects of the two strongly electron‐accepting DEE substituents rather than from extended π‐electron conjugation along the oligomeric backbone, as had previously been observed for DEE‐substituted porphyrins.     

Synthesis of Amphiphilic Fullerene Derivatives and Their Incorporation in Langmuir and Langmuir‐Blodgett Films

Various amphiphilic fullerene derivatives were prepared by functionalization of [5,6]fullerene‐C₆₀‐I_h (C₆₀) with malonate or bis‐malonate derivatives obtained by esterification of the malonic acid mono‐esters 5 – 7 . Cyclopropafullerene 10 was obtained by protection of the carboxylic acid function of 6 as a tert‐butyl ester, followed by Bingel addition to C₆₀ and a deprotection step (Scheme 2). The preparation of 10 was also attempted directly from the malonic acid mono‐ester 6 under Bingel conditions. Surprisingly, the corresponding 3′‐iodo‐3′H‐cyclopropa[1,9][5,6]fullerene‐C₆₀‐I_h‐3′‐carboxylate 11 was formed instead of 10 (Scheme 3). The general character of this new reaction was confirmed by the preparation of 15 and 16 from the malonic acid mono‐esters 13 and 14 , respectively (Scheme 4). All the other amphiphilic fullerene derivatives were prepared by taking advantage of the versatile regioselective reaction developed by Diederich and co‐workers which led to macrocyclic bis‐adducts of C₆₀ by a cyclization reaction at the C‐sphere with bis‐malonate derivatives in a double Bingel cyclopropanation. The bis‐adducts 37 – 39 with a carboxylic acid polar head group and four pendant long alkyl chains of different length were prepared from diol 22 and acids 5 – 7 , respectively (Scheme 9). In addition, the amphiphilic fullerene derivatives 45, 46, 49, 54 , and 55 bearing different polar head groups and compound 19 with no polar head group were synthesized (Schemes 11–13, 15, and 5, resp.). The ability of all these compounds to form Langmuir monolayers at the air‐water interface was investigated in a systematic study. The films at the water surface were characterized by their surface pressure vs. molecular area isotherms, compression and expansion cycles, and Brewster‐angle microscopy. The spreading behavior of compound 10 was not good, the two long alkyl chains in 10 being insufficient to prevent aggregation resulting from the strong fullerene‐fullerene interactions. While no films could be obtained from compound 19 with no polar head group, all the corresponding amphiphilic fullerene bis‐adducts showed good spreading characteristics and reversible behavior upon successive compression/expansion cycles. The encapsulation of the fullerene in a cyclic addend surrounded by four long alkyl chains is, therefore, an efficient strategy to prevent the irreversible aggregation resulting from strong fullerene‐fullerene interactions usually observed for amphiphilic C₆₀ derivatives at the air‐water interface. The balance of hydrophobicity to hydrophilicity was modulated by changing the length of the surrounding alkyl chains or the nature of the polar head group. The best results in terms of film formation and stability were obtained with the compounds having the largest polar head group, i.e. 45 and 46 , and dodecyl chains. Finally, the Langmuir films obtained from the amphiphilic fullerene bis‐adducts were transferred onto solid substrates, yielding high‐quality Langmuir‐Blodgett films.     

2‐Amino‐4‐(4‐chlorophenyl)‐7,7‐dimethyl‐5‐oxo‐5,6,7,8‐tetrahydro‐4H‐chromene‐3‐carbonitrile

The supramolecular structure of the title compound, C₁₈H₁₇ClN₂O₂, is determined by the intersection of two chains formed by N—H⋯O and N—H⋯N hydrogen bonds, forming a two‐dimensional sheet.     

Low- and high-conversion studies of the free radical copolymerization of 2-hydroxyethyl methacrylate with styrene in N,N′-dimethylformamide solution

2-Hydroxyethyl methacrylate (HEMA) and styrene (S) have been copolymerized in a 3 mol · L⁻¹N,N′-dimethylformamide (DMF) solution using 2,2′azobis (isobutyronitrile) (AIBN) as an initiator over a wide composition and conversion range. From low-conversion experiments and ¹H-NMR analysis, the monomer reactivity ratios were determined according to the Mayo–Lewis terminal model. The comparison of the obtained results with those previously reported for copolymerization in bulk and in toluene reveals a relatively small but noticeable solvent effect that can be qualitatively explained by the bootstrap model. Cumulative copolymer composition as a function of conversion is satisfactorily described by the integrated Mayo–Lewis equation; overall copolymerization rate increases with increasing the HEMA/S ratio, and individual monomer conversion is closely related to the monomer molar fraction in the feed. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2941–2948, 1999     

High-Yielding Enantioselective Synthesis of the Macrolactam Aglycon of Sch 38516 from Two Units of (2R)-2-Ethyl-4-penten-1-ol

The same precursor —namely, (2R)-2-ethyl-4-penten-1-ol—was used to obtain fragments C9–C13 and C1–C8 of 1 , the aglycon of Sch 38516 (which is active against Candida sp.) and fluvirucin B₁ (which is active against influenza A virus). The key steps of the synthesis were the aldol-like reaction between the two fragments and the macrolactamization of a 13-azidotridecanoic acid derivative (see scheme). MOM=methoxymethyl, Py=2-pyridyl.     

ortho‐Fluoroazobenzenes: Visible Light Switches with Very Long‐Lived Z Isomers

Improving the photochemical properties of molecular photoswitches is crucial for the development of light‐responsive systems in materials and life sciences. ortho‐Fluoroazobenzenes are a new class of rationally designed photochromic azo compounds with optimized properties, such as the ability to isomerize with visible light only, high photoconversions, and unprecedented robust bistable character. Introducing σ‐electron‐withdrawing F atoms ortho to the N?N unit leads to both an effective separation of the n→π* bands of the E and Z isomers, thus offering the possibility of using these two transitions for selectively inducing E/Z isomerizations, and greatly enhanced thermal stability of the Z isomers. Additional para‐electron‐withdrawing groups (EWGs) work in concert with ortho‐F atoms, giving rise to enhanced separation of the n→π* transitions. A comprehensive study of the effect of substitution on the key photochemical properties of ortho‐fluoroazobenzenes is reported herein. In particular, the position, number, and nature of the EWGs have been varied, and the visible light photoconversions, quantum yields of isomerization, and thermal stabilities have been measured and rationalized by DFT calculations.