Commuting Toeplitz operators on the Segal-Bargmann space

Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily.     

The atomic structural dynamics of γ-Al2O3 supported Ir-Pt nanocluster catalysts prepared from a bimetallic molecular precursor: a study using aberration-corrected electron microscopy and X-ray absorption spectroscopy

This study describes a prototypical, bimetallic heterogeneous catalyst: compositionally well-defined Ir-Pt nanoclusters with sizes in the range of 1-2 nm supported on γ-Al(2)O(3). Deposition of the molecular bimetallic cluster [Ir(3)Pt(3)(μ-CO)(3)(CO)(3)(η-C(5)Me(5))(3)] on γ-Al(2)O(3), and its subsequent reduction with hydrogen, provides highly dispersed supported bimetallic Ir-Pt nanoparticles. Using spherical aberration-corrected scanning transmission electron microscopy (C(s)-STEM) and theoretical modeling of synchrotron-based X-ray absorption spectroscopy (XAS) measurements, our studies provide unambiguous structural assignments for this model catalytic system. The atomic resolution C(s)-STEM images reveal strong and specific lattice-directed strains in the clusters that follow local bonding configurations of the γ-Al(2)O(3) support. Combined nanobeam diffraction (NBD) and high-resolution transmission electron microscopy (HRTEM) data suggest the polycrystalline γ-Al(2)O(3) support material predominantly exposes (001) and (011) surface planes (ones commensurate with the zone axis orientations frequently exhibited by the bimetallic clusters). The data reveal that the supported bimetallic clusters exhibit complex patterns of structural dynamics, ones evidencing perturbations of an underlying oblate/hemispherical cuboctahedral cluster-core geometry with cores that are enriched in Ir (a result consistent with models based on surface energetics, which favor an ambient cluster termination by Pt) due to the dynamical responses of the M-M bonding to the specifics of the adsorbate and metal-support interactions. Taken together, the data demonstrate that strong temperature-dependent charge-transfer effects occur that are likely mediated variably by the cluster-support, cluster-adsorbate, and intermetallic bonding interactions.     

Monitoring the status of T-cell activation in a microfluidic system

Leukocyte adhesion to the endothelium through surface molecules such as E-selectin and intercellular adhesion molecule-1 (ICAM-1) is a critical cellular event reflecting the physiological status of both cell types. Here we present a microfluidic system that can not only easily monitor the interaction between leukocytes and endothelial cells under physiological conditions, but also screen drug candidates for potential modulation of this interaction. Shear stress, which is an important factor for the binding of activated T cells to tumor necrosis factor-alpha (TNF-α)-treated human umbilical vein endothelial cells (HUVECs), was easily controlled by adjusting the flow rate in the microfluidic system. Whole blood of patients with systemic lupus erythematosus (SLE) who have auto-reactive T cells were infused into the activated HUVECs which subsequently showed a higher level of binding compared to a control blood sample from a person without SLE. When these autoreactive T cells were treated with immunosuppressors tacrolimus and cyclosporin A, the binding of the T cells to HUVECs was dramatically decreased. Therefore, this microfluidic system is capable of differentiating the physiological status of T cells or endothelial cells representing different disease conditions, as well as being useful for the identification of novel reagents that modulate the functions of leukocytes or endothelial cells.     

Pep-1 Peptide-modified liposomal carriers for intracellular delivery of gold nanoparticles

A Pep-1 peptide-modified liposomal (Pep1-Lipo) carrier system was investigated to increase the intracellular delivery of gold nanoparticles (Au NPs). Au NPs with a mean diameter of 13 nm were successfully encapsulated into the inner aqueous compartment of the novel carrier using an ethanol injection technique, reserving the distinctive optical characteristics of the surface plasmon resonance peak around 530 nm. The Au NP-loaded liposomal carrier was physically characterized as 150-170 nm in size and 45 mV in zeta potential. Dark field microscopic observation demonstrated that in vitro cellular association and/or translocation of the nanoprobes into the cells was increased by Pep1-Lipo carriers compared to bare Au NPs. In conclusion, this novel liposomal formulation is a promising platform for the intracellular delivery of metallic nanoprobes including Au NPs.     

Influence of TiO2 nanotube morphology and TiCl4 treatment on the charge transfer in dye-sensitized solar cells

Dye-sensitized solar cells (DSSCs) were fabricated using TiO₂ nanoparticles (NPs), TiO₂ nanotube arrays (NTAs), and surface-modified NTAs with a TiCl₄ treatment. The photovoltaic efficiencies of the DSSCs using TiO₂ NP, NTA, and TiCl₄-treated NTA electrodes are 4.25, 4.74, and 7.47 %, respectively. The highest performance was observed with a TiCl₄-treated TiO₂ NTA photoanode, although in the case of the latter two electrodes, the amounts of N719 dye adsorbed were similar and 68 % of that of the NP electrode. Electrochemical impedance measurements show that the overall resistance, including the charge–transfer resistance, was smaller with NTA morphologies than with NP morphologies. We suggest that a different electron transfer mechanism along the one-dimensional nanostructure of the TiO₂ NTAs contributes to the smaller charge–transfer resistance, resulting in a higher short circuit current (J _sc), even at lower dye adsorption. Furthermore, the TiCl₄-treated NTAs showed even smaller charge–transfer resistance, resulting in the highest J _sc value, because the downward shift in the conduction band edge improves the electron injection efficiency from the excited dye into the TiCl₄-treated TiO₂ electrodes.     

Preparation of submicron‐scale,electrospun cellulose fibers via direct dissolution

Cellulose nonwoven mats of submicron‐sized fibers (150 nm–500 nm in diameter) were obtained by electrospinning cellulose solutions. A solvent system based on lithium chloride (LiCl) and N,N‐dimethylacetamide (DMAc) was used, and the effects of (i) temperature of the collector, (ii) type of collector (aluminum mesh and cellulose filter media), and (iii) postspinning treatment, such as coagulation with water, on the morphology of electrospun fibers were investigated. The scanning electron microscopy (SEM) and X‐ray diffraction studies of as‐spun fibers at room temperature reveal that the morphology of cellulose fibers evolves with time due to moisture absorption and swelling caused by the residual salt and solvent. Although heating the collector greatly enhances the stability of the fiber morphology, the removal of salt by coagulation and DMAc by heating the collector was necessary for the fabrication of dry and stable cellulose fibers with limited moisture absorption and swelling. The presence and removal of the salt before and after coagulation have been identified by electron microprobe and X‐ray diffraction studies. When cellulose filter media is used as a collector, dry and stable fibers were obtained without the coagulation step, and the resulting electrospun fibers exhibit good adhesion to the filter media. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1673–1683, 2005     

Brownian dynamics simulations of star-branched polymers in dilute solutions in extensional flow

Using Brownian dynamics (BD) simulations of FENE bead-spring models, the dynamics of star-branched polymers in dilute solutions under extensional flow have been investigated. Studies on star polymers in transient extensional flow reveal that the initial transient stress response at low strains is governed by both the number of arms and the shortest arm. On the other hand, the steady-state behavior of star polymers in elongational flow is limited by the maximum effective “contour” length of the molecules. The distribution of arm extension and birefringence of the star-branched molecule are broader and the mean is shifted to lower values, when compared to equivalent linear systems. As a result, the degree of arm extension at steady-state decreases as the number of arms in the star increases. Both an analysis of individual ensembles in Brownian dynamics simulations and a study of a simple force balance indicate that the constraint imposed on the star arms by the central branch point and contributions from “asymmetric” arm arrangements give rise to overall less extended and oriented star-branched molecules with broader arm extension and birefringence distributions. The results obtained from stress-conformation hysteresis simulation indicate that less-stretched arms exhibit more retarded relaxation, as the number of arms increases in star-branched molecules. The effect of excluded volume (EV) interactions, incorporated through the Lennard–Jones potential, on the dynamics of star polymers in extensional flow appears unimportant.     

Templated synthesis of silver nanoparticles in amphiphilic poly(vinylidene fluoride‐co‐chlorotrifluoroethylene) comb copolymer

In this study, poly(vinylidene fluoride‐co‐chlorotrifluoroethylene)‐graft‐poly(oxyethylene methacrylate), P(VDF‐co‐CTFE)‐g‐POEM, an amphiphilic comb copolymer with hydrophobic P(VDF‐co‐CTFE) backbone and hydrophilic POEM side chains at 73:27 wt % was synthesized. The POEM side chains were grafted from the P(VDF‐co‐CTFE) mainchain backbone via atom transfer radical polymerization (ATRP) using direct initiation of the chlorine atoms in CTFE units. Synthesis of microphase‐separated P(VDF‐co‐CTFE)‐g‐POEM comb copolymer was successful, as confirmed by nuclear magnetic resonance (¹H NMR), FTIR spectroscopy, and transmission electron microscopy (TEM). Nanocomposite films were prepared using the comb copolymer as a template film and the in situ reduction of AgCF₃SO₃ precursor to silver nanoparticles under UV irradiation. Silver nanoparticles with 4–8 nm in average size were in situ created in the solid state template film, as revealed by TEM, UV–visible spectroscopy, and wide angle X‐ray scattering (WAXS). Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) presented the selective incorporation and the in situ growth of silver nanoparticles within the hydrophilic POEM domains of microphase‐separated comb copolymer film. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 702–709, 2008