Directional Newton methods in variables

Directional Newton methods for functions of variables are shown to converge, under standard assumptions, to a solution of . The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of with maximal modulus. These methods are applied to solving systems of equations without inversion of the Jacobian matrix.

     

Envelope Theorems in Dynamic Programming

The envelope theorem is a statement about derivatives along an optimal trajectory. In dynamic programming the envelope theorem can be used to characterize and compute the optimal value function from its derivatives. We illustrate this here for the linear-quadratic control problem, the resource allocation problem, and the inverse problem of dynamic programming.     

Water-soluble surface-anchored gold and palladium nanoparticles stabilized by exchange of low molecular weight ligands with biamphiphilic triblock copolymers

A study is presented of the stabilization of gold and palladium nanoparticles (NPs) via a place-exchange reaction. Au and Pd NPs of approximately 3.5 nm were prepared by a conventional method using tetraoctylammonium bromide (TOAB) as the stabilizing agent. The resulting nanoparticles, referred to as Au-TOAB or Pd-TOAB, were later used as templates for the replacement of TOAB ligand with poly(ethylene oxide)- b-polystyrene- b-poly(4-vinylpyridine) (PEO- b-PS- b-P4VP) triblock copolymer. This biamphiphilic triblock copolymer was synthesized by atom transfer radical polymerization (ATRP) with control over the molecular weight and polydispersity. The place-exchange reaction was mediated through strong coordination forces between the 4-vinylpyridine copolymer and the metal species located on the surface of the nanoparticles. In addition, the displacement of the outgoing low molecular weight TOAB ligands by high molecular weight polymers is an entropy-assisted process and is believed to contribute to stabilization. The prepared complex, polymer-NP, exhibits greatly improved stability over the metal-NP complex in common organic solvents for the triblock copolymer. Self-assembly in water after ligand exchange resulted in micellar structures of about approximately 20 nm (electron microscopy) with the metal NP found located on the surface of the micelles. The stability of the nanoparticles in water was shown to depend greatly on the grafting density of the copolymer, with high stability (more than 6 months) at high grafting density and low stability, accompanied with irreversible agglomeration, at relatively low grafting densities. The surprising location of the metal NP (for both Au and Pd) on the surface of the micelles in water is explained by the fact that, upon self-assembly in THF/water system, the most hydrophobic chains (i.e., PS) undergo self-assembly first at low water content forming the core, followed by the P4VP (whether or not associated with the metal) forming a shell, and finally the PEO forming the corona. In lower metal content assemblies, the P4VP chains located in the shell undergo swelling in an acidic medium causing a substantial increase in micellar corona size, as confirmed by dynamic light scattering measurements. The present study offers a simple approach for the stabilization of various metal nanoparticles of catalytic interest, using a unique polymeric support that can be dispersed in organic solvents as well as aqueous solutions.     

Molecular Flow and Lanthanum -Catalyzed Bond Interchange in Sodium Phosphate Polymers

Abstract

It is observed that sodium phosphate polymers, in which some of the Na⁺ ions have been replaced by La³⁺ ions, are subject to both simple molecular flow and to bond interchange in the glass transition region. These two relaxation mechanisms are separated, and their relative contributions to the shear viscosity are calculated. It is shown that the bond-interchange mechanism is subject to an activation energy of ca. 50 kcal, while that of the molecular flow is of the order of 200 kcal at Tg + 30°C;the latter is of the WLF form. It is further shown that the La³⁺ ions act as cross-links, at least at low concentrations, and that bond interchange occurs at the site of the La³⁺ ions rather than at random along the polymer chain.     

Towards Eumelanin@Zeolite Hybrids: Pore‐Size‐Controlled 5,6‐Dihydroxyindole Polymerization

5,6‐Dihydroxyindole ( 1 ) and its N‐methyl derivative ( 2 ), key eumelanin building blocks, were inserted into zeolite L by sublimation at 175 °C for 5 days. At a 10 mg/300 mg indole/zeolite ratio, the resulting hybrids displayed a stable deep red coloration. CP/MAS ¹³C NMR and UV/Vis spectroscopy of the red species suggested the generation and accommodation of quinonoid biindole derivative(s) within the void space of the acidic zeolite channels. Removal of the zeolite matrix by treatment with HF gave a stable species that could be separated by HPLC and characterized by mass spectrometry as an oxygenated biindole derivative (or a mixture of isomers), suggesting addition of water to the original dimer and subsequent re‐oxidation. The characterization was corroborated by optimized molecular geometries and simulated UV spectra with density functional calculations. Loading 1 or 2 into the larger pores of SBA‐15 type mesoporous silica resulted in black eumelanin‐type polymers, confirming channel size dependence over the polymerization process.     

Phase separation of micellar solutions at extreme dilution: A study of polystyrene-b-poly(sodium acrylate) micelles in aqueous NaCl solutions

Micellar solutions of polystyrene-b-poly(sodium acrylate) copolymers in aqueous NaCl were studied by static light scattering (SLS). It was found that micellar solutions of the copolymer, at concentrations of NaCl at, or above, 2.0 mol dm⁻³, became turbid on dilution at constant salt concentration and at constant temperature. Turbidity arose from highly dilute solutions (typically at a concentration three orders of magnitude lower than the overlap concentration of the micelle, C*), but at concentrations above the expected critical micellization concentrations (c.m.c.s). The observed turbidity was attributed to the phase separation of the micellar phase. A systematic investigation of the phase separation phenomenon was performed. The effects of various parameters on the solution behavior of the micellar solutions were studied, including the effect of the concentration of NaCl, the effect of temperature, and the effect of the length of the hydrophilic, corona-forming poly(sodium acrylate) block. Phase separation was attributed to the presence of a very large excess of NaCl in the dilute micellar solutions. It was proposed that phase separation arose because of the reduced hydration of the polyion, the decreased electrostatic repulsion between the micelles, and the increase in the amount of ion binding, which occur in highly dilute salt solutions. © 1996 John Wiley & Sons, Inc.     

Effects of acyl donor type, catalyst type, and reaction conditions on the activity and selectivity of Friedel-Crafts acylation

Acylation of anisole and 3-methylanisole was performed with several acylating reagents (acetylation by AcCl and Ac₂O and bromoacetylation by BrAcCl and (BrAc)₂O) over different solid acid catalysts. The reaction conditions were optimized with respect to the acylation reagent, overall yield, solid acid catalyst, and the products selectivities. While acylation of anisole with acetyl chloride or acetic anhydride resulted in its full conversion to para-substituted acetophenone, the use of bromoacetyl bromide or bromoacetic anhydride yielded also the ortho-substituted product. Acylation of 3-methylanisole also yielded both para- and ortho-substitutions, and the products distribution was affected by the reaction conditions and catalyst type. It was found that while more acidic catalysts (caesium salt of heteropolyacid and zeolites) were the most active towards anisole acylation, the most active catalysts for the acylation of 3-methylanisole were ion-exchange catalysts. Employing HY-740 zeolite resulted in the highest ortho-selectivity in the acylation of anisole with bromoacetyl bromide and bromoacetic anhydride and in the acylation of 3-methylanisole with acetic anhydride.     

Thiol-terminated monolayers on oxide-free Si: assembly of semiconductor-alkyl-S-metal junctions

Self-assembled monolayers formed by thermal hydrosilylation of a trifluoroacetyl-protected alkenylthiol on Si-H surfaces, followed by removal of the protecting groups, yield essentially oxide-free monolayers suitable for the formation of Si-C11H22-S-Hg and Si-C11H22-S-Au junctions in which the alkyl chains are chemically bound to the silicon surface (via Si-C bonds) and the metal electrode (via Hg-S or Au-S bonds). Two barriers to charge transport are present in the system: at low bias the current is temperature activated and hence limited by thermionic emission over the Schottky barrier in the silicon, whereas as at high bias transport is limited by tunneling through the organic monolayer. The thiol-terminated monolayer on oxide-free silicon provides a well-characterized system allowing a careful study of the importance of the interfacial bond to the metal electrode for current transport through saturated molecules.