Employing (half-)titanocene complexes as initiators for the synthesis of end-functionalized polylactides by coordination polymerization

Seven (half-)titanocene alkoxide complexes, [Cp₂TiCl(OEt)], [Cp₂TiCl(O-2-Bu)], [Cp₂TiCl(OCH₂CF₂CF₂H)], [CpTiCl₂(OEt)], [CpTiCl₂(O-(S)-2-Bu)], [CpTiCl₂(OCH₂CF₃)], and [Cp₂TiCl(OCH₂CF₃)], were synthesized and employed in lactide coordination polymerization. These organotitanium (IV) compounds proved to be very efficient initiators for the ring-opening polymerization of enantiomeric l -lactide and racemic mixture of rac-lactide, leading to end-functionalized polymers. Kinetic studies illustrated that these compounds produce well-defined polymers in a controlled manner. This was further demonstrated by synthesizing poly(l -lactide-b-hexyl isocyanate) diblock copolymer. The effect of the alkoxy end groups on the thermal behavior of the polymers was also studied by thermogravimetric analysis and differential scanning calorimetry. The polymers were characterized using size exclusion chromatography and proton nuclear magnetic resonance spectroscopy. The optical properties of the diblock copolymer were also investigated. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2192–2202     

Sample restriction using radiofrequency field selective pulses in high-resolution solid-state NMR

In this article a method is suggested for restricting a sample (spatial localization) by preparing the magnetization with a phase-modulated radiofrequency pulse which inverts magnetization only over a very narrow range of radiofrequency field strengths. This is the most efficient method, in terms of sensitivity, of restricting the sample to improve rf homogeneity. The method is demonstrated by using it to improve the resolution obtained in a homonuclear dipolar decoupling experiment.     

Two-dimensional high-resolution NMR spectra in matched B(0) and B(1) field gradients

In a recent publication we presented a method to obtain highly resolved NMR spectra in the presence of an inhomogeneous B(0) field with the help of a matched RF gradient. If RF gradient pulses are combined with "ideal" 90 degrees pulses to form inhomogeneous z rotation pulses, the line broadening caused by the B(0) gradient can be refocused, while the full chemical shift information is maintained. This approach is of potential use for NMR spectroscopy in an inhomogeneous magnetic field produced by an "ex-situ" surface spectrometer. In this contribution, we extend this method toward two-dimensional spectroscopy with high resolution in one or both dimensions. Line narrowing in the indirect dimension can be achieved by two types of nutation echoes, thus leading to depth-sensitive NMR spectra with full chemical shift information. If the nutation echo in the indirect dimension is combined with a stroboscopic acquisition using inhomogeneous z-rotation pulses, highly resolved two-dimensional correlation spectra can be obtained in matched field gradients. Finally, we demonstrate that an INEPT coherence transfer from proton to carbon spins is possible in inhomogeneous B(0) fields. Thus, it is possible to obtain one-dimensional (13)C NMR spectra with increased sensitivity and two-dimensional HETCOR spectra in the presence of B(0) gradients of 0.4 mT/cm. These schemes may be of some value for ex-situ NMR analysis of materials and biological systems.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

An optimal Hardy–Morrey inequality

In this work we improve the sharp Hardy inequality in the case p?>?n by adding an optimal weighted H?lder seminorm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for p?>?n and the Hardy inequality, the latter having the best constant.     

A variational principle for adaptive approximation of ordinary differential equations

Summary A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error=local errorweight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms. Mathematics Subject Classification (2000):65L70, 65G50This work has been supported by the EU–TMR project HCL # ERBFMRXCT960033, the EU–TMR grant # ERBFMRX-CT98-0234 (Viscosity Solutions and their Applications), the Swedish Science Foundation, UdelaR and UdeM in Uruguay, the Swedish Network for Applied Mathematics, the Parallel and Scientific Computing Institute (PSCI) and the Swedish National Board for Industrial and Technical Development (NUTEK).     

On the large time behavior of the heat kernels of quasiperiodic differential operators

We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the L^p boundedness of the associated Riesz transform operators.     

Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere

We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations, we derive new vector Yang–Baxter map and integrable discrete vector sine-Gordon equation on a sphere.     

A Bioorthogonal Small‐Molecule‐Switch System for Controlling Protein Function in Live Cells

Chemically induced dimerization (CID) has proven to be a powerful tool for modulating protein interactions. However, the traditional dimerizer rapamycin has limitations in certain in vivo applications because of its slow reversibility and its affinity for endogenous proteins. Described herein is a bioorthogonal system for rapidly reversible CID. A novel dimerizer with synthetic ligand of FKBP′ (SLF′) linked to trimethoprim (TMP). The SLF′ moiety binds to the F36V mutant of FK506‐binding protein (FKBP) and the TMP moiety binds to E. coli dihydrofolate reductase (eDHFR). SLF′‐TMP‐induced heterodimerization of FKBP(F36V) and eDHFR with a dissociation constant of 0.12 μM . Addition of TMP alone was sufficient to rapidly disrupt this heterodimerization. Two examples are presented to demonstrate that this system is an invaluable tool, which can be widely used to rapidly and reversibly control protein function in vivo.     

Synthesis of 2D Germanane (GeH): a New,Fast, and Facile Approach

Germanane (GeH), a germanium analogue of graphane, has recently attracted considerable interest because its remarkable combination of properties makes it an extremely suitable candidate to be used as 2D material for field effect devices, photovoltaics, and photocatalysis. Up to now, the synthesis of GeH has been conducted by substituting Ca by H in a β‐CaGe₂ layered Zintl phase through topochemical deintercalation in aqueous HCl. This reaction is generally slow and takes place over 6 to 14 days. The new and facile protocol presented here allows to synthesize GeH at room temperature in a significantly shorter time (a few minutes), which renders this method highly attractive for technological applications. The GeH produced with this method is highly pure and has a band gap (E_g) close to 1.4 eV, a lower value than that reported for germanane synthesized using HCl, which is promising for incorporation of GeH in solar cells.