Ring‐opening polymerization of ϵ‐caprolactone initiated with different ruthenium derivatives: Kinetics and mechanism studies

End‐functionalized polyesters have been synthesized by ring‐opening polymerization (ROP) of ?‐caprolactone (CL) initiated with five different ruthenium derivatives in the presence of a series of alcohols as transfer agents. Mechanistic studies were performed for ROP of CL with RuCl₂(PPh₃)₃ ( I ), TpRuCl(PPh₃)₂ ( II ), and TpRuCl(PHPh₂)(PPh₃) ( III ) as catalysts in the presence or absence of benzyl alcohol (BzOH). Obtained molecular weights are proportional to CL/BzOH ratio, but there is not a direct relationship with CL/ruthenium complex ratios. ¹H and ¹³C NMR spectroscopy revealed the existence of benzyl ester end‐groups. Catalysis involves (a) dissociation of ruthenium complexes, (b) coordination of the lactone CL, (c) coordination of the BzOH with the formation of a metal alkoxide, (d) transfer from the alkoxyl ligand to the coordinated lactone, and (e) ring‐opening of CL by oxygen‐acyl bond cleavage. The proposed mechanism is supported by ¹H, ¹³C, and ³¹P NMR, gel permeation chromatography (GPC), and MALDI‐TOF analysis of the polymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6926–6942, 2006     

Enhancement of the oxygen transfer in a circulating three-phase fluidized bed bioreactor

Applied Biochemistry and Biotechnology - The addition of α-alumina to the aqueous solution of sodium alginate for imobilization of viable cells allows the production of denser particles than...     

Excess molar enthalpies of the ternary system mtbe+ethanol+hexane

Excess molar enthalpies of the ternary mixture {x₁ tert-butyl methyl ether (MTBE)+x₂ ethanol+(1–x₁–x₂) hexane} and, the involved binary mixtures {x tert-butyl methyl ether (MTBE)+(1–x) ethanol}, {x tert-butyl methyl ether (MTBE)+(1–x) hexane} and {x ethanol+( 1–x) hexane} have been measured at 298.15 K and atmospheric pressure, over the whole composition range, using a Calvet microcalorimeter. The results were fitted by means of different variable degree polynomials.     

On the Fermat–Weber center of a convex object

We show that for any convex object Q in the plane, the average distance from the Fermat–Weber center of Q to the points in Q is at least Δ(Q)/7, where Δ(Q) is the diameter of Q, and that there exists a convex object P for which this distance is Δ(P)/6. We use this result to obtain a linear-time approximation scheme for finding an approximate Fermat–Weber center of a convex polygon Q.     

Amino acid-functionalized cyclopentadienyl molybdenum tricarbonyl complex and its use in catalytic olefin epoxidation

The complex [(N-benzyloxycarbonylprolyl)cyclopentadienyl]-Mo(CO)₃Me was prepared by the reaction of the amino acid-functionalized cyclopentadienyl-lithium reagent with Mo(CO)₆, and subsequent methylation with CH₃I. The complex was characterized by FTIR, ¹H and ¹³C NMR, and elemental analysis. A single-crystal X-ray diffraction study showed that the complex is chiral, crystallizing in the orthorhombic P2₁2₁2₁ space group with the Flack parameter refining to –0.007(16), which unequivocally confirms the presence of an enantiomerically pure compound. The complex was examined as a catalyst precursor in the liquid-phase epoxidation of trans-β-methylstyrene at 280–330 K, using either tert-butylhydroperoxide (tert-BuOOH), cumylhydroperoxide or urea-hydrogen peroxide adduct as oxidant, and, optionally, a co-solvent. With chloroform and tert-BuOOH, the catalytic activity surpasses that previously reported for chiral complexes of the type CpMo(CO)₃X, giving the epoxide isomers ((R,R)-(+) and (S,S)-(?)-1-phenylpropylene oxide) in excellent selectivity, albeit with negligible enantiomeric excess. FTIR spectroscopy showed that the oxidative decarbonylation of the tricarbonyl complex with tert-BuOOH is fast under the reaction conditions used, and that the structural integrity of the amino acid-functionalized cyclopentadienyl group is retained during this process. The use of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate as a solvent for the catalyst generates a biphasic liquid–liquid reaction system that enables, at the end of a catalytic cycle, the separation and reutilization of the catalyst.     

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

An increase of the coupling strength in the system of two coupled R?ssler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings on the surfaces of unstable tori, whereas transition from phase to lag synchronization is preceded by a decrease in the number of unstable periodic orbits.     

Decoherence and the rate of entropy production in chaotic quantum systems

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.     

Extensible Embeddings of Black-Hole Geometries

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner–Fronsdal local isometric embedding of the corresponding black hole geometry. Allowing for globally non-trivial embeddings, living in Kaluza–Klein-like M ₅ × S ₁ (rather than in standard Minkowski M ₆ ) and parametrized by some wave number k, extensibility can be achieved for apparently forbidden frequencies in the range ₁ (k) ₂ (k). As k 0, _{1, 2} (0) _H (e.g., _H = 1/4M in the Schwarzschild case) such that the Hawking–Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza–Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding gauge field.     

Nuclear spin-lattice and nuclear spin-spin relaxation time measurements in EuB6 at low temperatures using the spin-echo technique

Experimental results on the nuclear spin-lattice and nuclear spin-spin relaxation times in the ferromagnetic EuB₆ at temperatures below 4·2 K are presented using the external magnetic field,H _ext, in the range of 0 ⩽H _ext ⩽ 10 kG. Nuclear spin-spin relaxation time computed on the basis of the Suhl-Nakamura process turns out to be 3·2μs, which compares well with the experimental value 11·1μs obtained with the 10 kG magnetic field at 1·7 K. It is found that in the ferromagnetic EuB₆,T ₁ is approximately 5 × 10³ times larger thanT ₂ at 1·7 K with the 10 kG magnetic field. Thus the effect ofT ₁ onT ₂ can be neglected. From the experimental value ofT ₂, the value of the homogeneous line broadening is found to be 14 kHz. The corresponding value obtained from the cw method is 175 kHz. This evidently shows the presence of the inhomogeneous line broadening in the cw NMR.     

Novel cerium(IV) heteropolyoxotungstate containing two types of lacunary Keggin anions

A novel V-shaped polyoxotungstate is formed when Ce(IV) metal centres bridge monolacunary [PW(11)O(39)](7-) anions to an unusual 1,4-bilacunary [PW(10)O(38)](11-) anion which appears with an unprecedented bridging structural motif.